Smart antennas are essential to increase the spectral efficiency of wireless communication systems. They can be realized by an antenna array at the base station and sophisticated base-band signal processing. Thereby, adaptive directional reception is achieved on the uplink and adaptive directional transmission on the downlink if channel knowledge is available at the transmitter. Hence, an increased antenna gain and an increased diversity gain are realized towards the desired user. At the same time, less interference is received from the other directions on the uplink or transmitted in the other directions on the downlink if channel knowledge is available at the transmitter. Therefore, more users can be accommodated by the system and a corresponding increase of the spectral efficiency is achieved. Even higher spectral efficiencies can be obtained if antenna arrays are not only used at the base station but also at the mobile. The theoretical capacity of such multiple-input–multiple-output systems has been shown to grow linearly with the size of the antenna arrays in sufficiently rich multi-path environments. Open problems in this new area of wireless communications include better and more realistic propagation models as well as improved algorithms for transmission and reception which approach the theoretical limits of the channel.