Only in the world of classical music can something 50 years old be considered "modern!"
There's a lot of very good 20th & 21st century music out there that you never hear just because it's unfamiliar. (Of course as with anything, there's the 90% that's crap.)
You could do a lot worse than
this introduction to 20th century concert music (written by a former teacher; includes "top 100" list).
EDIT: I mean a former teacher
of mine.