Physical layer security is an emerging technique to improve the wireless communication security, which is widely regarded as a complement to cryptographic technologies. To design physical layer security techniques under practical scenarios, the uncertainty and imperfections in the channel knowledge need to be taken into consideration. This paper provides a survey of recent research and development in physical layer security considering the imperfect channel state information (CSI) at communication nodes. We first present an overview of the main information-theoretic measures of the secrecy performance with imperfect CSI. Then, we describe several signal processing enhancements in secure transmission designs, such as secure on-off transmission, beamforming with artificial noise, and secure communication assisted by relay nodes or in cognitive radio systems. The recent studies of physical layer security in large-scale decentralized wireless networks are also summarized. Finally, the open problems for the on-going and future research are discussed.