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In this paper, the authors give an overview of wireless communication systems using multiple transmit and multiple receive antennas. The authors first introduce the theoretical capacities of these systems. Then the authors present the main families of spatio-temporal codes and their associated decoding algorithms. These codes allow to exploit the multiplexing and diversity gain of the multiple antenna systems. Then the authors show that space time codes associated to channel codes can achieve performance close to the capacity of the multiple antenna systems. The authors also consider frequency selective channels, where it is possible to combine the space time codes with the OFDM technique. Finally the authors give some of the possible applications of space time coding.