I am trying to write another chapter for my history book: post 1975. The only thing I'm able to say for sure is that the period officially begins with Glass' Einstein on the Beach (1976). The Wikipedia article Contemporary classical music describes the following active movements:
Modernism is represented by Pierre Boulez, Luigi Nono, Karlheinz Stockhausen, Milton Babbitt, Charles Wuorinen, Sir Harrison Birtwistle, Thomas Adès and Gunther Schuller, among others.
Computer music, including computer generated music. Can computer generated music be said to be composed? Computers have their fingers in everywhere these days, but specific names are irrelevant. The electronic music festival in SF falls here.
Spectral music is represented by a long list of people no one has ever heard of. This is a type of computer music where structure derives from timbre. The term was coined by Hugues Dufourt.
Post-modernism is chiefly characterized by its opposition to modernism (whatever that means) and is represented by John Adams, Luciano Berio, John Cage, John Corigliano, George Crumb (of whale music fame), Brian Eno, Henryk Górecki, Steve Reich and Alfred Schnittke. If you recognize many of these names, you will see that this is not at all a style of music but a political movement.
Polystylism is exactly what it sounds like, and is represented by Sir Peter Maxwell Davies, Sofia Gubaidulina and Alfred Schnittke, among others. In fact most modern composers may be considered polystylists, so ....
Historicism, referring to earlier periods of classical music. None of these names are familiar to me except Peter Schickele who is parodying Bach.
Neo-romanticism is represented by John Williams, John Corigliano, Gian Carlo Menotti, Ellen Zwilich and the later works of Krzysztof Penderecki and György Ligeti.
Art rock influence is represented by another long list of composers I have never heard of.
"World music" influence has actual historical precedents, and consists of bring in styles from other cultures, such as the work of Béla Bartók and later Olivier Messiaen. This isn't World Music per se, but rather the incorporation of world music into a classical music context.
New Simplicity is represented by Henryk Górecki and Arvo Pärt.
New Complexity involves extensions to standard notational practice and is represented by another list of people I don't know.
Minimalism and post-minimalism is represented by Philip Glass, John Adams, Steve Reich and Terry Riley, among others. We don't have to explain this, do we?
Extended techniques are any funny thing you do with standard instruments. Col legno is an example where you play the violin with the stick part of the bow. Lots of people do this.
Generative music involves the inclusion of non-musical sounds in musical compositions and is a term invented by Brian Eno. This movement is mysteriously missing from the Wikipedia article. This refers to taped sounds which can be subsequently manipulated electronically. I have encountered this in the work of Lynn Job. Crumb's whales were all created on more or less normal musical instruments.
You see the problem. Music schools are having trouble deciding what to teach students about composition. My friends and I have decided that schools can only teach the techniques of the past, counterpoint from the Renaissance and Baroque, sonata form from the classical period, principles of orchestration from the romantic period, etc.
It should be obvious what this means. Something that was formerly an integral part of a culture is now purely an intellectual exercise. It means that classical music is dead.