Channel estimation is conceived for hybrid MIMO communication systems. Mean square error minimization and MI maximization are used as our performance metrics and a pair of low-complexity channel estimation schemes are proposed. In each scheme, the training sequence and the analog matrices of the transmitter and receiver are jointly optimized. We commence by designing the optimal training sequences and analog matrices for the first scheme. Upon relying on the resultant optimal structures, the training optimization problems are substantially simplified and the nonconvexity resulting from the analog matrices can be overcome. In the second scheme, the channel estimation and data transmission share the same analog matrices, which beneficially reduces the overhead of optimizing the associated analog matrices. Therefore, a composite channel matrix is estimated instead of the true channel matrix. By exploiting the statistical optimization framework advocated, the analog matrices can be designed independently of the training sequence. Based on the resultant analog matrices, the training sequence can be efficiently designed according to diverse channel statistics and performance metrics. Finally, we conclude by quantifying the performance benefits of the proposed estimation schemes.