Two of the key plaintiffs are Paul Katami and Jeff Zarrillo, a Burbank, California, couple who want to marry but can't because of Proposition 8.

CNN: SHARE THIS

"This is about our freedom and our liberty, " Katami said.

CNN: Day Two of same-sex marriage at Supreme Court

One of the plaintiff couples -- Paul Katami and Jeff Zarrillo of Burbank, California, who want to marry but can't because of Proposition 8 -- contend the state is discriminating against them because of their sexuality.

CNN: Day Two of same-sex marriage at Supreme Court