This paper presents recent progress and prospects for the Muon Collider as a next-generation collider facility following the High Luminosity LHC program. With capabilities for high-energy muon collisions, the Muon Collider opens the door to a wide range of physics opportunities, particularly in Higgs boson studies and beyond. A overview of the current status of the facility is presented focusing on the recent progress obtained by the International Muon Collider Collaboration. The main challenges, and the future technological developments are discussed.