As wearable devices become more ingrained in our daily lives, traditional communication networks primarily designed for human being-oriented applications are facing tremendous challenges. The upcoming 5G wireless system aims to support unprecedented high capacity, low latency, and massive connectivity. In this article, we evaluate key challenges in wearable communications. A cloud/edge communication architecture that integrates the cloud radio access network, software defined network, device to device communications, and cloud/edge technologies is presented. Computation offloading enabled by this multi-layer communications architecture can offload computation-excessive and latency-stringent applications to nearby devices through device to device communications or to nearby edge nodes through cellular or other wireless technologies. Critical issues faced by wearable communications such as short battery life, limited computing capability, and stringent latency can be greatly alleviated by this cloud/edge architecture. Together with the presented architecture, current transmission and networking technologies, including non-orthogonal multiple access, mobile edge computing, and energy harvesting, can greatly enhance the performance of wearable communication in terms of spectral efficiency, energy efficiency, latency, and connectivity.