Recent breakthroughs in artificial intelligence (AI) give rise to a plethora of intelligent applications and services based on machine learning algorithms such as deep neural networks (DNNs). With the proliferation of Internet of things (IoT) and mobile edge computing, these applications are being pushed to the network edge, thus enabling a new paradigm termed as edge intelligence. This provokes the demand for decentralized implementation of learning algorithms over edge networks to distill the intelligence from distributed data, and also calls for new communication efficient designs in air interfaces to improve the privacy by avoiding raw data exchange. This paper provides a comprehensive overview on edge intelligence, by particularly focusing on two paradigms named edge learning and edge inference, as well as the corresponding communicationefficient solutions for theiRecent breakthroughs in artificial intelligence (AI) give rise to a plethora of intelligent applications and services based on machine learning algorithms such as deep neural networks (DNNs). With the proliferation of Internet of things (IoT) and mobile edge computing, these applications are being pushed to the network edge, thus enabling a new paradigm termed as edge intelligence. This provokes the demand for decentralized implementation of learning algorithms over edge networks to distill the intelligence from distributed data, and also calls for new communication efficient designs in air interfaces to improve the privacy by avoiding raw data exchange. This paper provides a comprehensive overview on edge intelligence, by particularly focusing on two paradigms named edge learning and edge inference, as well as the corresponding communicationefficient solutions for their implementations in wireless systems. Several insightful theoretical results and design guidelines are also provided. © 2022, Beijing University of Posts and Telecommunications. All rights reserved.