SCOTUS is hearing argument in Obergefell v. Hodges et all today on two questions presented:
1. Does the Fourteenth Amendment require a state to license a marriage between two people of the same sex?
2. Does the Fourteenth Amendment require a state to recognize a marriage between two people of the same sex when their marriage was lawfully licensed and performed out-of-state?
You can listen to the oral arguments on the SCOTUS website.
[Edit] If you don't want to listen to the whole argument SCOTUSblog has made a 30 min audio super cut.
If you are interested you can read all the merits briefs on the American Bar Association webpage here.
SCOTUSBlog has a analysis of the arguments up here.