A wider coverage and a better solution to latency reduction in 5G necessitates its combination with mobile edge computing (MEC) technology. Decentralized deep learning (DDL) as a promising solution to privacy-preserving data processing for millions of edge smart devices, it leverages federated learning within the networking of local models, without disclosing a client's raw data. Especially, in industries such as finance and healthcare where sensitive data of transactions and personal medical records is cautiously maintained, DDL facilitates the collaboration among these institutes to improve the performance of local models, while protecting data privacy of participating clients. In this survey paper, we demonstrate technical fundamentals of DDL for benefiting many walks of society through decentralized learning. Furthermore, we offer a comprehensive overview of recent challenges of DDL and the most relevant solutions from novel perspectives of communication efficiency and trustworthiness.