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This article provides an overview of the signal processing techniques used to enhance secrecy in the physical layer of multiantenna wireless communication systems. Motivated by results in information theory, signal processing techniques in both the data transmission and the channel estimation phases have been explored in the literature to enlarge the signal quality difference at the destination and the eavesdropper. In the data transmission phase, secrecy beamforming and precoding schemes are used to enhance signal quality at the destination while limiting the signal strength at the eavesdropper. Artificial noise (AN) is also used on top of beamformed or precoded signals to further reduce the reception quality at the eavesdropper. In the channel estimation phase, training procedures are developed to enable better channel estimation performance at the destination than at the eavesdropper. As a result, the effective signal-to-noise ratios (SNRs) at the two terminals will be different and a more favorable secrecy channel will be made available for use in the data transmission phase. Finally, future research directions are discussed.