Cognitive radio networks (CRNs) offer a promising solution for spectrum scarcity problem by means of dynamic spectrum access. So long as in highly dynamic environments, the secondary user (SU) communication is often interrupted, spectrum mobility is a key feature enabling continuous SU data transmission. Namely, SU performs spectrum handoff by transferring ongoing communication to a vacant channel. This article discusses some important features of spectrum mobility in CRNs. Qualitative comparison of various handoff strategies is considered with regard to handoff latency. Furthermore, essential design issues and associated research challenges are also addressed.