Multiple input multiple output (MIMO) antenna is at core of the presently available wireless technologies. The design of MIMO antennas over a limited space requires various approaches of mutual coupling reduction, otherwise gain, efficiency, diversity gain, and radiation patterns will be severely affected. Various techniques have been reported in literature to control this degrading factor and to improve the performance of the MIMO antennas. In this review paper, we have carried out an extensive thorough investigation of diversity and mutual coupling (correlation) reduction techniques in compact MIMO antennas.