Cognitive radio (CR) is one of promising techniques to alleviate the spectrum scarcity resulting from the increasing demand for wireless services and the exclusive spectrum allocation policy. CR allows unlicensed users (secondary users) to access the under-utilized spectrum assigned to licensed users (primary users) if quality-of-service (QoS) requirements of primary users can be satisfied. However, the performance of secondary users' communications is severely degraded by the QoS constraints imposed on the secondary users for the primary users. Diversity techniques for the secondary users help overcome the performance degradation by mitigating or exploiting the fluctuation of fading channels. We overview recent results on diversity techniques in CR and discuss fundamental limits and gains of diversity techniques in CR systems.