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The efficacy of channel modeling and training for multiple-input multiple-output (MIMO) time-varying flat faded Rayleigh channels is studied herein from the information-theoretical perspective. To characterize the channel dynamics in wide-sense stationary uncorrelated scattering wireless environments, proper autoregressive (AR) channel models for different fading speeds are discussed from the viewpoints of the mean squared error (MSE) and Bayesian Cramér-Rao lower bound (BCRB) of channel estimation. Furthermore, the training efficacy is examined with the achievable capacity when the MSE of channel estimation attains the BCRB. Our numerical simulations show that neither is the first-order AR model enough, nor is a large-order AR model needed for modeling time-varying fading channels. The analysis on BCRB also shows that the influence of the multiple access interference among transmit antennas is not negligible for channel estimation in time-varying fading channels even if using orthogonal sequences for training. As channel tracking can utilize the current and all past training symbols, the optimal training lengths for each data packet may be less than the number of transmit antennas. These results help re-examine the efficacy of model complexity and training overhead, and characterize the achievable rate for MIMO systems that use more practical methods in estimating Rayleigh fading channels. [ABSTRACT FROM AUTHOR]