Best Way to Integrate Subwoofers?

What’s the best way to integrate subwoofers with monitors, or speakers?

I’m not referring to placement, or room treatments. I’m referring to what’s the best way to integrate via a crossover, without a custom dedicated crossover.

Do you run two separate signals to the subs vs the speakers and supress the lower frequencies to the speakers, while supressing the upper frequencies to the subs? It would seem that this method might allow you to move the crossover to higher frequencies, relying more on the subs for the bass and lower mids - if that is beneficial. It would also seem that this method would permit you to taylor the slope of the crossover to minimize overlap of frequencies between the subs and the speakers, which might improve clarity - depending on the capability of the particular crossover used. And, I suppose it implies / requires a separate crossover to be used to run both signals through to route the mids and highs only to the speakers and the bass and lows only to the subs.

Or do you run the same signal to the subs and speakers and just emphasize the subs up to the bottom of the frequency range of the speakers, crossing over from the subs to the speakers at that point (crossover notch). It would seem that this method would require you to fix the crossover at the bottom of the frequency range of the speakers, wherever that may be, and would not require a separate crossover to be inserted into the signal path. And it would seem to imply that the slope of the crossover would be limited to the slope inherent in the subs and speakers, which would limit the flexibility of the crossover.

Or, does it make any difference?
Active crossovers between the pre-amp and amp is the best way imo.

You run interconnects from the pre-amp or dac to the subs, then from the subs to the amp. Only the high pass goes to the speakers. You then can adjust the phase and crossover point. I find steep 24 dB slopes work best for sub crossovers.

JL audio’s Cheaper E112/110 have a decent one built in that works well. The kicker is you lose the room correction with the E-sub line compared to the fathom line.

JL audio make an external one that is very good and works with any brand but it is pricey. i am sure there are other options I just don’t know of them.
Crossover point is very speaker dependent BUT I have pretty much always found it best to cross-over where the mains bass  driver hits minimum motion. Meaning where the bass driver’s output drops off and the port picks up. For many speakers this is 50hz-ish give or take. 

You can run the speaker lower but most of the time the sub is much better than your speakers below 50z (even large good passive speakers). This also frees up the main amp to not work as hard and take vibrations out of your mains. 

Saddly large speakers work better with subs than small speakers. They blend better and the power-band hand off is better too. 
I prefer using a high pass filter to the speakers. Some prefer running the speakers full range. It all depends on the speakers that you are using with the sub!
So... if you use an external crossover (other than the one, which may be built in to the sub) - do you insert it after the subs?  I guess that location would use the sub controls to adjust the curve of the subs, and the external crossover to adjust the curve of the mains?