20th Century Composers

Sugarbrie - I'm with you on all your choices. I would like to add a few that are conspiciously missing:

Jean Sibelius
Claude Debussy (could be considered 19th Century but a truly influential and original composer of the modern era)
Maurice Ravel (among the best orchestrators of any period)

The most influential composer of the 20th Century and the greatest in my book is Igor Stravinsky

I agree with the Debussy. He actually wrote what could be called the first music in "20th century style" the "Prelude a l'apres-midi d'un faune" or Prelude of an afternoon of a fawn. It broke the lock of the romantic style and paved the way for others to take changes.

Ok so to answer the posed question (at last), for me: Coltrane, Stravinsky, Glass

I am currious. How was Philip Glass influential? To whom? Anyone? What is his legacy?

Webern, Webern, Webern..... egads gentlemen. Every major
artistic, serious composer in the 20th century is absolutely indebted to him.In particular Stravinsky when he finally found out about serial music. If you wanted to remove yourself from romantic/classical musical forms, you just looked at a Webern score. Schoenberg may have started serial music (subset of atonal music, Ives' music would be another form), but it was Webern who took it to its logical conclusion. Serious art music of the 20th century was Webern's century. The only serious contender would have to be Bartok but he was unique and his style was not copied to any great extent, but his string quartets are still one of the finest sets of chamber music produced in the the 20th C.