Does the Senate approve US Supreme Court nominations?

They have the power to confirm or reject nominations to the US Supreme Court.

The only control the Senate has over the US Supreme Court is their exercise of "advice and consent," that allows them to confirm or reject the President's nominee for a vacancy on the Court. Confirmation requires a simple majority (51%) affirmation of the Senators voting. Short of a vote, the minority political party may also filibuster or threaten to filibuster in an attempt to get the nominee's name withdrawn from consideration.