Exploiting spatial diversity and space time codes, multi-input multi-output (MIMO) communication systems provide high spectral efficiency and low bit error rate. Therefore, these systems have attracted much attention in the last decade. MIMO communication systems rely strongly on the channel state information. So, channel estimation is an essential step in implementation of these systems and different estimation methods such as training based, blind and semi-blind schemes have been proposed according to channel time variations. In this thesis, channel model for MIMO communication systems under various frequency and time fading states is studied. A few training based estimation methods and the corresponding most desirable training sequences that minimize the mean square error (MSE) are introduced. Also, time variation of the channel and some tracking methods in time varying channels are studied. Then, the effect of considering spatial correlation among different sub-channels in the estimation and tracking of channel coefficients are investigated. In the case of block fading channels, a method in which the output of the least square estimator is exploited to estimate the channel correlation matrix and noise variance with the same training sequences is proposed. Using the MMSE estimator, the effect of appropriate deployment of the channel correlation matrix in reducing the estimation error compared to the methods that ignore correlation among different sub-channels is investigated. Also, in the case of non-block fading channels, considering spatial correlation in addition to the temporal correlation among sub-channels, state-space model of the channel is modified and the effect of this modification in decreasing the channel tracking error is presented via computer simulations.