Smart antennas in the form of beam-forming, spatial multiplexing and MIMO have been widely used in wireless communication networks to enhance data rates, increase coverage and mitigate interference. Various communication standards such as WiMAX and LTE support the use of multiple antennas to enhance quality of transmission and reception of signals. As smart antennas exploit the spatial dimension to increase network capacity, this has been considered as a promising technique to meet ever increasing demand on radio spectrum. Recently, cognitive radios have also emerged as a potential technique to enhance the efficiency of spectrum usage. While we witness spectrum scarcity for emerging high data rate wireless applications, various spectrum occupancy measurements have indicated that large portions of the spectrum bands are unoccupied most of the time indicating underutilization of spectrum. Cognitive radio technology is considered as an essential enabling disruptive technology for facilitating dynamic spectrum access thereby resolving spectrum crisis due to the under-utilization of spectrum. Cognitive users (also known as secondary users) will be allowed to opportunistically use the licensed spectrum owned by the primary users provided that the secondary user transmissions do not harmfully affect the primary network. This talk will address coexistence of secondary users and primary users through appropriate interference mitigation mechanisms using smart antennas. The talk will start with a brief introduction to smart antennas and their benefits. Application of smart antennas to mitigate interference in a cognitive radio network will be covered followed by an outline on various mathematical optimization techniques for the design of smart antennas in cognitive radio networks.