Music which has inappropriate lyrics is one issue.
The Shulchan Aruch in O”C 560 Paskens like the Gemara (Gittin 7a) that music is Assur as a Zecher L’Churban. This would seem to include all music. There are many Heterim given by many different Poskim for many reasons. They are too numerous to actually list here but suffice it to say that if you listen to music you most likely have someone to rely on.