Cognitive radio transmissions in the presence of channel uncertainty are considered. In practical scenarios, cognitive secondary users need to perform both channel sensing in order to identify whether the channel is being occupied by the primary users or not, and also channel estimation in order to learn the channel fading coefficients. Generally, errors occur in both channel sensing and estimation, and this leads to a coupling between the two. More specifically, imperfect sensing affects both the structure and the performance of channel estimation schemes. With this motivation, the interactions between channel sensing and estimation are studied in this paper. In particular, different channel estimation schemes including minimum mean-square error (MMSE), linear MMSE, and mismatched MMSE estimations are analyzed, and their dependence on sensing decisions and their performances are investigated.