Cognitive radio (CR) is a promising solution to improve the spectrum utilization by enabling unlicensed users to exploit the spectrum in an opportunistic manner. Spectrum handoff is a different type of handoff in CR necessitated by the reappearance of primary user (PU) in the licensed band presently occupied by the secondary users (SUs). Spectrum handoff procedures aim to help the SUs to vacate the occupied licensed spectrum and find suitable target channel to resume the unfinished transmission. The purpose of spectrum mobility management in cognitive radio networks is to make sure that the transitions are made smoothly and rapidly such that the applications running on a cognitive user perceive minimum performance degradation during a spectrum handoff. In this paper, we will survey the literature on spectrum handoff in cognitive radio networks.