BluRay and normal DVD, how do they swap?

I dont have a BluRay player yet, so I want to understand how it all works b4 I cough up the cash. Can you play a regular DVD in a BluRay player? Can you play a BluRay disc in a regular DVD player(of course, without the picture quality)? About 15 years or more ago I bought a CDI player that was supposed to be the new big thing. Big mistake, it didnt take off like everyone expected & I dont want to have that happen to me again! That was about $500 that is down the drain. Ouch.