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