What are the age requirements for appointment to the US Supreme Court?

There are no age requirements for Supreme Court justices. In fact, unlike candidates for Congress and the Presidency, there are no constitutional requirements at all. This doesn't mean the President could nominate a 10-year-old; he's (or she's) expected to select someone with appropriate qualifications, or the Senate will reject the nomination.

This is what happened when former President George W. Bush nominated White House Counsel Harriet Miers for a position on the Supreme Court. The American Bar Association declared her unqualified, the Senate Judiciary Committee protested, and her name was formally withdrawn.

Most US Supreme Court justices are appointed while in their 40s and 50s.