Don't quite know what your definition of modern music is, but current music there is some great stuff being made. First Aid Kit - Swedish harmony duo, touch of Country, but more leaning towards melodic pop. Michael Kiwanuka - old school Soul with some very modern twists, Ezra Collective - funky Jazz, Little Simz - Hip Hop meets old James Bond theme music, Christine & the Queen's - don't know how to categorise but melodic, electronic dance, pop etc.
I'm 59 and loving more new music in the last couple of years than I have for ages. Give BBC 6 Music a try.