The state of the art and the recent progress made in Muon Catalyzed Fusion is reviewed. Over 100 dt fusions per muon were experimentally observed, while the most reliable value for dt sticking is ~ 0.6%. The theory describes now all kinetic processes with high precision and predicts very large rates for dμt formation at collision energies ∊μt ≈ 0.1 - 2 cV. For future exploration of this phenomenon, the use of H/D/T triple mixtures is suggested. In energy applications, the concept of the Muon Catalyzed Hybrid Reactor is discussed, especially in the context of combining it for uranium breeding with the electronuclear channel.