The edge cache is an effective way to reduce the heavy traffic load and the end-to-end latency in radio access networks (RANs) for supporting a number of critical Internet of Things (IoT) services and applications. It has been verified to provide high spectral efficiency (SE), high energy efficiency (EE), and low latency. Along with several key techniques that have been applied, such as device-to-device communication and predictive caching, the edge cache techniques in RANs for IoT are becoming diversified. This paper comprehensively surveys the recent advances of the edge cache in RANs, including the key techniques and the corresponding performances. In particular, the key techniques are presented from the viewpoints of the deployment location of edge caches, content placement strategy, and coded caching. An advanced hierarchical edge cache structure is presented, and the main impacts on SE, EE, and latency of the key techniques are mainly summarized. Several open issues and challenges are identified as well to spur future investigations, in which the joint optimization of radio and cache resources, the edge cache with mobile edge computing and network intelligence, privacy, and security are discussed.