To address the coverage and capacity challenges in fifth-generation (5G) wireless networks, the relay technique has been considered as a promising solution and recently attracted great attentions from academia. The multiway relay channel (mRC), which serves as a fundamental building block of a relay network, defines the family of all possible information-flow patterns between a relay node and its neighboring nodes. Combined with several new techniques, such as physical-layer network coding (PLNC), signal and interference alignments, multi-input multi-output (MIMO), etc., the mRC exhibits superior capability to assist multiuser information exchange. In this article, we aim to provide a comprehensive overview on the state-of-the-art of the mRC from the perspectives of both information-theoretic and communication-theoretic studies. The key results are summarized and discussed to identify the current research progress of the mRC. Open problems and research challenges are also discussed to spur future research towards the mRC.