Abstract:Massive Black Holes (MBHs) in galactic centers are believed to be described by the Kerr metric with only two parameters (mass and spin; no-hair theorem). The distribution of those MBHs on the mass and spin plane contains rich information on the MBH growth history. In this talk, I will report our recent investigations on the spin evolution of MBHs under various accretion processes. We show that different accretion modes (e.g., coherent, chaotic, or tidal star accretion) result in quite different spin distribution. Assuming a two phase accretion model, an initial coherent accretion followed by a later chaotic accretion phase, we use the current available spin measurements to obtain constraints on the MBH growth history and discuss future prospects for such constraints . I will also talk about the possible correlation between the radiative efficiency of QSOs and the MBH mass.