Engaging users is a priority for designers of products and services of every kind. The need to understand users' experiences has motivated a focus on user engagement across computer science. However, to date, there has been limited review of how Human-Computer Interaction and computer science research interprets and employs the concept. Questions persist concerning its conception, abstraction, and measurement. This article presents a systematic review of engagement spanning a corpus of 351 articles and 102 definitions. We map the current state of engagement research, including the diverse interpretation, theory, and measurement of the concept. We describe the ecology of engagement and strategies for the design of engaging experiences, discuss the value of the concept and its relationship to other terms, and present a set of guidelines and opportunities for future research.