Why have capacitors improved so much over the years?

Assuming they have, which is my general impression…
I don't know much, but I would guess it's a result of materials research and testing as well as more precise manufacturing and better lead wires.
Specifically, though… Any amp builders or speaker builders to describe the tech?
Tech is nothing more than a physical description of the ways they are different. Why they got better is audiophiles obsessed with and driven to achieve exceptional sound quality. How  they got better was by trying out and evaluating different ideas by listening.
good question, like OP, I would like to know what ... is better and why about capacitors specifically.

Switching from electrolytic capacitors to film caps has brought the focus on the materials used in the construction of capacitors. Electrolytics can sound poor because the insulator is actually an oxidized plate. Basically a capacitor is two plates separated by an insulator. Film caps allow that form of construction. Using high purity metal foils and Teflon insulators without the need to use a paste to oxidize a plate improves the transmission of a purer music signal.
I am not sure the best capacitors today vs 15-20 years ago are in fact better. It seems to me there is now a market for high grade fancy capacitors in the DIY hifi community, and so there are some smart companies who are riding that wave and marketing to that audience.

Dueland, for instance. It would be interesting to hear from people who have been in the high end hifi manufacturing business for a long time, hear their commentary on this. There seem to be some others on this forum who will do modifications to some gear for a fee, using these fancy branded caps and other components. Things like salt used to just be salt. Now there is Himalayan salt, Moldon salt, etc etc. It is still just salt, and before there were better quality and worse quality salt for cooking, the marketing business just had not latched on and did their thing.
I had my amp recapped 10 years ago with 60s era NOS Aerovox caps one of the best and cheapest upgrades I've ever done. So better technology maybe, better sound maybe maybe not.
If they have, and I wouldn’t doubt that they have, it is likely due to more precise computer aided design and robotic manufacture.
I've been modding for perhaps twenty years now, IME, both film and electrolytics have improved, I presume for all the reasons above. Really, very few choices years ago with boutique caps, most were general use variety. As I recall, the first audiophile grade film caps I used were from VH Audio, Duelund, Jantzen, Mundorf, seems like they all came to market in about the same range of time. So many brand choices today, way more values, voltages, metallurgy  available today. I've yet to hear a bad boutique film cap in my mod projects, only sq issue has been less than preferred colorations, large physical size sometimes makes fitting a chore.
It is still just salt
not sure you'd have a lot of chefs and gourmets in agreement... 

@jond - NOS capacitors, huh? Uh oh, another crazy rabbit hole! 

Why have capacitors improved so much over the years?

Not so with all caps

And as far as non-polarized (plastics etc) coupling caps go, the BEST CAP IS NO CAP, if the circuit allows for it to trim out any dc offset manually, or a simple dc servo can be installed. (direct coupled always sound better) but not all circuits can be dc coupled

As for polarized big or small electrolytic power supply caps go, some quality makes NOS (new old stock) can be very good, but very important they need to be "conditioned" first using an ac variac, over a couple of hours and bought up from zero very slowly to their max voltage.

Cheers George
Vintage Japan Man collectors pay their weight in Gold Pressed Latinum for formed and working 50’s production TCC Metal and Super Metalpack paper in oils.....

Some good answers. Many new cap technologies driven by military applications primarily. New materials and improved manufacturing processes. Electrolytics have gotten smaller, but basically unchanged, still used because they are cheap. Capacity/cost.
Capacitors have improved in certain ways due to designers looking and wanting a different type of sound than previous versions. The change in sound is due to using different materials and construction. I can say that the early capacitors due not sound bad at all if given time to re form in an old component. You have to give some time before you judge an old capacitor especially in an amplifier or speaker because most of the time they are not bad at all they just need time to play and re form. If you do change the capacitor to a new one it can sometimes cause the gear or speaker in question to sound very different, especially bright at first, due to the new cap needing to form as well.
I don't know the specific answer to this question but generally all manufacturing processes have taken great steps forward.  Thinking about things unrelated to stereo, such as cars and microwaves, I find that well made, name brand examples are much more reliable and much more precision made.  Just compare the car you had when you were a kid to now (unless you're still a kid).  think about what your expectations were with 100,000 miles on it were then (hope to make it there without major component failure) to now (100,000 miles is just broken in for many vehicles).  so it doesn't surprise me that capacitors are better and thanks for pointing this out with a good question. 

The best are still vacuum dielectric or air dielectric. They’ve been around forever, but they come in small values at high cost. I use these exclusively in my phono / pre.

Film and foil are next best; styrene is pretty neutral, teflon a bit bright, polypropylene a bit dull. Some examples are ’very’ rather than ’a bit’.

Metallized are constructed by depositing metal onto the dielectric. Quality appears to depend on the thickness of the metal and the junction of the metal to the wire leads. They can be almost as good as film and foil, or almost as bad as electrolytic. Mica and teflon are the best.

Ceramics tend to be inferior to metallized, the quality seeming to depend on the dielectric constant of the ceramic, lower being better.

I don’t have strong opinions on paper in oil, but I really don’t like leaks, so I avoid them.

Good luck!  YMMV

The big difference is in manufacturing tolerances.  Back in my early days in electronics (60s) 5% or even 10% tolerances in values were frequently used because it cost money to get to 1% tolerance or better.  MilSpec parts often had to measure far more accurately than consumer electronics.  The same was true for inductors and resistors.  The simple truth is that a 50 microfarad capacitor that accurately measure as 50 mfd will sound the same as any other that accurately measures as 50mfd.  Depending on the values of the other components in the circuit you cannot hear the difference, assuming they are all accurate to a given tolerance.  Usually, the differences in rated voltage and tolerance are used for the purposes of obtaining longevity and reducing failures due to arcing which results in a short circuit.

The other truth is that snake oil salesmen are far better psychologists than most university PHDs.  They have been around a long time because they know their craft and it works.  
WOW!  Short Answer!  "manufacturing process and technology, engineering !"  Hmm, Why are micro processors, HDD's and now SDD's Smaller Nowadays?? or the iPhone has a zillion more processing power than the computer that took us to the Moon..  Hmm, the Capacitor question is a Great one, I'll do a tad more research on that.. 
Barjohn, that's the engineer's answer from 1980.

The book that changed all that was Horowitz and Hill, 'The Art of Electronics', which had a table of capacitors and their actual characteristics. With real information about the physical effect known as 'Dielectric Absorption', or DA, applied to everyday electronic components, the stage was set for a genuine improvement in sound quality.

There are a few topologies which sound good and don't much profit from better components, but the best ones can be much improved thereby. In my experience, anyway.

Build yourself a breakout box in which you can change an important cap from one technology to another with the flick of a switch. Get a book on psychology experiments to learn how to do a single-blind experiment, and recruit your lady as a test subject. I think you'll get quite a surprise.
Here is a person who has done a lot of subjective testing with many different brands and types of capacitors. Might be worth reading before diving headlong into capacitor rolling. It saved me a lot of time and money.

Since capacitors are ubiquitous in all electronics, the statement, “Why they got better is audiophiles obsessed with and driven to achieve exceptional sound quality” is inane. To suggest that  our niche industry would be the driver of such improvements is just silly. 
@terry9 thanks for your thoughtful replies. Can you give an example of great air dielectric capacitor?
@puffball08 - I used that database to pick new caps for one of my amps, very informative.  Quite an undertaking…

Obviously, better manufacturing in general will lift all boats, but clearly the audiophile niche is highly active and innovative to some degree beyond mere marketing.  The premium audiophiles will pay has to explain the R&D that goes into VCaps or Mundorf or Duelund or whatever, and there must be legit technical advances happening, whether proprietary or otherwise.
First off the capacitors of the past are not all around today.  Think Black Gate capacitors which I feel were the best capacitors back then and today but they are no longer manufactured.  Materials have not really changed but now manufacturers are using different materials then they did back in the day.  Same goes with cables.  Silver, copper, aluminum combinations, twisting, insultation, etc.  Even the cheap Sprague capacitors lasted a long time.

What is different is more of the wire used.  Dueland makes hybrid copper and silver capacitors.  Could not find that back in the day.

So to me it is more of the types of materials being used and yes, some are made better than others - think V-Caps.  They are a really good manufactured product.  As referred to above with parts swappers - you can change the sound by installing larger power supply capacitors think Nichicon and Mundorf.  Anyone of you can do this as there is generally two leads for solder wires onto - just make sure there is enough room for the larger caps.

So what has changed to me is the materials used, etc.  BUT some of these caps can elevate you systems sound considerably.  V-Caps especially.  

For resistors - Audio Note now only offers non-magnetic resistors.  A step up from their now discontinued resistors.  Plus they also are now manufacturing a Silver resistor.  Expensive but worth it.

Happy Listening.

Richard Marsh published an article in Audio Magazine in 1980 that detailed the range of parasitic loss factors inherent in capacitors. Dialectric Absorption and Dissipation Factor in films, and Equivalent Series Resistance in electrolytics. He compared mylar, polystyrene and polypropylene and teflon films and found each had a distinct effect on how a circuit sounds. The race was truly on after that. Prior to this publication only Mark Levinson was featuring Wima caps, but soon everyone was going boutique. I think military, aerospace, and medical equipment advances created the market and audio was an accidental beneficiary at first. 
Around 1978 or 79 I had a gentleman answer a for sale ad I had posted for an Audio Research preamp. He made an unusual request of me. He professed to be the owner of a company that was prototyping a preamp of his design. He asked if it would be possible to compare his prototype to my SP6. Who would turn that idea down? He arrived with his unit that was basically just his boards and electronics. A true early stage build. I didn't expect much. I was wrong. We spent a couple of hours using my system and comparing the two preamps to one another. I only remember that he was convinced his sounded more musical and that he was concerned that his choice of capacitors was in need of change. He explained to me what he was listening for concerning the caps. At the time I thought it was "out there" that he would be sitting in his lab and listening to various caps. He must have done something right because his company is still in business and still selling a highly regarded preamp. 
Everything has improved over the years.
Defects introduce colorations.
Some prefer the colorations.
Who was it? Not much of a story without the name.
It’s market driven. Who cared about capacitors 20 or 30 years ago. People like us who tweek and upgrade electronics have found that capacitors make a difference in sound quality. Like changing tubes and interconnects.
Engineers who designed professional gear 40 and 50 years ago cared. Back then I knew some then 'old timers' who were aware. Can't comment on earlier, but no doubt some were aware.

I had a tube 'guru' tweak my Citation II with better resistors, caps & wire. Same cct & old tubes, but OMG.
jfd11, hmmm, you have to tell us the name or it's like it never happened. 
Redwood, I bought most of mine from Surplus Sales of Nebraska, when I didn't make my own.

At the Surplus Sales website, click on 'capacitors' in the left column, then on 'air gap variable', then go to the 'quad' section. There are some with 4 sections, each of which maxes at 460pf, for about 1.9nF or 0.0019 uF when paralleled. With judicious design, one can create an RIAA network with values in that range.

Warning: they're big and expensive. But it's the best sound available.
@ieales - thanks for the link, cool history.

@terry9 thats a wild website… I have no idea what I’m even looking at with those air caps!
My visitor was Ken Stevens of  Convergent Audio Technology. His wife, I believe was from the WNY area.
Redwood, it’s just a matter of getting used to them. Capacitance is an effect of two conductors separated by an insulator. The bigger the plates (conductors), the more capacitance. The closer together, the bigger the capacitance.

Accordingly, the capacitors are made so that every other plate is connected together, and the shaft turns the plates so that they become close together and alternating. This increases capacitance to the maximum value, while turning past that place decreases the capacitance towards the minimum.

With the help of a meter you’ll figure it out in a few minutes. Nothing exotic here, the theory’s been known for 200 years.
Since you seem to be interested, one of the best books you can buy is an edition of Art of Electronics by Horowitz and Hill. First edition 1980, third edition just a few years ago.
I have no idea what I’m even looking at with those air caps!

No one does. Nor does it matter. What matters is how they perform. As determined by listening. Which is what I said in the beginning.

If the real question is not why but which this is how you go about finding your caps- study this. Everything you need to know. http://www.humblehomemadehifi.com/Cap.html This was my main resource for upgrading my crossovers. (Thank you, Rick.)
While the referenced page is extensive, it's also a lot of hooey as components perform in concert with their containing circuit. There is no absolute and cost is seldom an arbiter of quality.

More than once, "Wow!" devolved
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@millercarbon - that link has been posted in this thread already.  The original question was actually “why” though…
"Why" was answered in the third post.
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Please define "improved".

In terms of sound quality, I do not think much has changed.  30 year old polystyrene caps were excellent, they still are.

If however, you are referring to their reliability, closer tolerances and higher temperature ratings, then yes, the more modern ones have greatly improved relative to their counterparts.

I want to submit perhaps it's equal part capacitors and equal part tweeter performance which has greatly improved.
@cakyol so you think it's all hype? 
Not just capacitors. Chips, transistors, resistors... almost all electronic components had been improved over the years.
Btw, in terms of capacitors, electrolytic capacitors been improved greatly.
I have not been involved in the engineering of any audio product but If I were, I would insure that that no corners were cut on the electronics. Unfortunately I think capacitors are generally the weak-link especially in Class A amps and any given product is only as good as its weakest link. If there were a way to eliminate capacitors, that would be miraculous.
BTW...salt is not "just salt". Salt absorbs minerals from the water in which it forms. Those varying minerals give salts different flavors. Not to mention the differences in the salinity levels per volume of salt. Do a salt tasting; you'll be surprised at the differences you can taste.