Wider coverage and a better solution to a latency reduction in 5G necessitate its combination with multi-access edge computing (MEC) technology. Decentralized deep learning (DDL) such as federated learning and swarm learning as a promising solution to privacy-preserving data processing for millions of smart edge devices, leverages distributed computing of multi-layer neural networks within the networking of local clients, whereas, without disclosing the original local training data. Notably, in industries such as finance and healthcare where sensitive data of transactions and personal medical records is cautiously maintained, DDL can facilitate the collaboration among these institutes to improve the performance of trained models while protecting the data privacy of participating clients. In this survey paper, we demonstrate the technical fundamentals of DDL that benefit many walks of society through decentralized learning. Furthermore, we offer a comprehensive overview of the current state-of-the-art in the field by outlining the challenges of DDL and the most relevant solutions from novel perspectives of communication efficiency and trustworthiness.