Classical composition never stopped evolving:

• Steve Reich — pioneer of minimalism, using repeating patterns that gradually shift out of phase
• Arvo Pärt — created tintinnabuli, a stripped-down spiritual style that sounds like light passing through glass
• John Adams — writes operas about current events (Nixon in China, Doctor Atomic) using minimalism and orchestral grandeur
• Max Richter — bridges classical and electronic; his 8-hour "Sleep" album is made to be heard while sleeping

These composers are not writing museum music. They use the tools of classical tradition to say something new.