Multi-User (MU) Muliple Input-Multiple Output (MIMO) has become an essential technology to achieve IMT advanced requirements. Performance of limited feedback MultiUser MIMO in spatially and time correlated channels are investigated in this paper. A special attention is drawn to the case where users have the opportunity to adapt their codebooks as a function of their own channel statistics (i.e. transmit correlation, time correlation or channel imbalance in dual-polarized scenarios). New codebook designs are provided for various propagation conditions. We show by analytical derivations (e.g. sum-rate analysis) and confirm by simulations how those channel statistics can be efficiently exploited in the design of Multi-User MIMO schemes with very low feedback overhead and low complexity. Those approaches are currently strong candidates to boost performance of IEEE 802.16m way beyond IEEE 802.16e and 3GPP LTE.