Why over-sampling and filtering... and why not?

I wonder if you all might help me understand in layman's terms the OS and filtering question. Obviously, manufacturers added oversampling and filtering to their cd players to correct some perceived flaw in CD playback. What were they trying to correct?

Conversely, there seems to be a small but dedicated movement building players with either no oversampling or no oversampling and no filtering. Obviously, they believe there is some sonic advantage to doing this. What is the benefit in this case, and why did they give up on oversampling and filtering?

In short, what is one gaining and losing in each case?

Thanks all, John
Post removed 
An anti-aliasing filter is used during recording of the CD so that the inaudible higher frequencies don't run into the 44.1 kHz digital sampling signal. Often 20kHz was chosen as the filter cut-off. It was called a "brick wall" because everything above that frequency was filtered out. The rationale was that we couldn't hear anything above that frequency anyway. Although we can't hear that high, those higher frequencies do interact with frequencies that we can hear. It has been suggested that this is one of the reasons why CD's don't sound as true as analog. Early filters also had a serious phase shift.

With oversampling, the digital sampling circuit of 44.1kHz is increased. If it was 4X oversampling, then 4 X 44.1 equals 176.4kHz. The farther the sampling circuit is from the sound spectrum, the less of a need for a filter with its attendant problems. You could use a filter with a more gentle roll-off, or even no filter at all.

This information is courtesy of people who know more than I do. It's just things I've picked up over the years from Audiogon and other sources.
the move to no correction, pretty much has ended.