Edge learning has enabled the training of large-scale machine learning models on a big dataset by implementing data parallelism in multiple nodes. However, the iterative interaction generated by multiple learning nodes together with the considerable quantity of communication data on each interaction yields huge communication overhead, which greatly hinders the scalability of Edge Learning. In this chapter, we introduce the mainstream approaches to achieve communication efficiency of edge training, including compressing communication data, reducing the synchronous frequency, overlapping computation and communication, and optimizing the transmission network. Specifically, we propose two hybrid mechanisms for communication-efficient Edge Learning. The first one is QOSP that integrates gradient quantization for communication compression and overlap synchronization parallel for simultaneous computation and communication. The second mechanism improves communication efficiency during the aggregation of client-side updates by quantizing the gradients and exploiting the inherent superposition of radio frequency signals. Finally, we discuss the future directions of communication-efficient edge learning.