Limit theorems for random matrices

The review of some results on limit theorems for random matrices that have been obtained during the last 10 years in the joint research of A. N. Tikhomirov and F. Götze, with participation of PhD students D. Timushev and N. Alexeev is given. The author considers the rate of convergence in semi-circle law and in the Marchenko-Pastur law. Steins method for random matrices, the proof of circular law, and some limit theorems for powers and products of random matrices are described.