5G network is expected to support massive user connections and exponentially increasing wireless services, which makes network security unprecedentedly important. Unlike traditional security-guaranteeing techniques which rely heavily on cryptographic approaches at upper layers of the protocol stack, physical-layer security (PLS) solutions fully take advantages of the characteristics of wireless channels to degrade the received signal qualities at the malicious users, and realize keyless secure transmission via signal design and signal processing techniques. PLS avoids the difficulties in the distribution and management of secret keys, and provides flexible security levels through adaptive transmission protocol design. Moreover, PLS techniques match the features of 5G networks well. Therefore, the application of PLS to 5G networks is a promising solution to address the security threats. This article presents a comprehensive review of the state-of-the-art PLS techniques, and discusses their applications in 5G networks. We first summarize the principle and advantages of PLS techniques, and point out the reasons why PLS is suitable for 5G networks. Then, we review the existing PLS methods in literature, and highlight several PLS solutions that are expected to be applied in 5G networks. Finally, we conclude this article and figure out some further research directions.