I know these used to not be as popular as they are now, but are they really as good as the hype? I mean after all plenty of famous trainers have never used one right?

I think sometimes like with most other things history repeats itself. What might work now and be in style might not be a year from now, but at some point it all comes around again.

I've never heard of round pens being used-what is the supposed benefit to this? I can see that they would be a lot harder to make, and set up in blocks or stables. It would also stop horses choosing a corner to use for bathrooming, so I'm not sure all would like?

A round pen is used for training as the horse has no "corner" and thus has to round and soften, etc, etc. John Lyons brought them into style. Lots of people use them for short term turn out as they are pretty cheap and lightweight metal piping with a gate. They can also be expanded or made smaller by adding/removing panels. Normally it is used for longing, with or more commonly without an actual longe line, and especially for working green animals.

I still see them around, I've even used one for quite some time. They can be useful for keeping a trained horse on task, or keeping a green horse from possibly hurting themselves. The price has come down alot which helped make them more common as well.

Wow, round pens sound like they could be better then "square" pens. I think I will have a talk with my family about restructuring our pens.