This is too big a subject to cover in one post but I can still put up some pretty pictures. My interest in stage design comes from being blown away by the sets (or the influence of sets) in cartoons like "What's Opera, Doc?" and animated features like "Fantasia" and "Alice in Wonderland." The backdrop above is from "Guys and Dolls" (1950) but it also looks a lot like the street outside the stadium in "Baseball Bugs." Animation is full of theatrical influence.
Guys and Dolls was famous for its backdrops. Here's (above) a moody sketch of the sewer where the crap game took place. The designer made it seem immense, important and mysterious, like the interior of a cathedral.
I also like the sketches generated by theatrical costume designers. I say "sketches" because the real clothing seldom looks as good as the sketch it was derived from.
Set design went through a lot of drastic changes in the last 100 years. Here's a Russian design from the years immediately after the revolution. The chair in the middle gives us the scale. Russian modernists were incredibly inventive but their efforts came to an end almost overnight when Lenin decided that he preferred realism.
I'm not a fan of Hockney's swimming pool paintings but his stage design is interesting. Forget the simplistic vertical curtains in the design above. Look instead at the way he uses the orchestra pit as a set design element. He paints the floor white so the standing musicians in black look like sticks or spikes. In another picture (unseen) he blackens the floor so the black musicians are invisible then he puts bright red caps on them. In yet another one he underlights the musicians so they look like zombies. Nifty, huh?