The movie follows a cop named Sgt. John Spartan, played by Stallone, who was nicknamed "The Demolition Man" because everywhere he went things would blow, explode, or be destroyed. He was tracking an escaped fugitive named Simon Phoenix, played by Snipes. Phoenix had a bunch of hostages that he was threatening to kill when Spartan appeared on the scene. After Snipes made the building blow up Spartan was tried and convicted of killing the 20 or so hostages Phoenix had there. They used a new prison sentence on him by putting him into a deep freeze, or cryostasis, for 35 years. Simon Phoenix was also given the same fate for his crimes and frozen until he would get his parole hearing.
Ahead in the future, in the year 2032, Simon Phoenix breaks out of the CryoPrison. The world in the year 2032 is a lot different than world Phoenix is used to. It's a utopian society where everyone is happy and the cops no longer have guns, but Glow Sticks that knock out the offender non-lethally. Los Angeles, which has been renamed to San Angeles, is the residing place for the world's new savior Raymond Coctow and one of the first people Phoenix is looking for after breaking out of prison.
Unable to handle this old brand of criminal it's reluctantly decided the SAPD needs an old fashioned cop to arrest him. John Spartan is reawakened to take down the man who sent him to CryoPrison over 20 years later. He has a companion and love interest in a cop named Lenina Huxley, played by Sandra Bullock, to help him navigate this new world and help take down Simon Phoenix. Huxley also has, what her friends describe, as an unhealthy fascination with the 20th century. This makes her a perfect balance to Spartan who while doesn't fully understand her fascination with it tried to figure it out anyway.
"Simon says die!" -- Simon Phoenix
"You are fined one credit for violation of the Verbal Morality Statute."