•Hybrid simulation is a new but rapidly growing area in operational research.•The main application areas are healthcare, manufacturing and supply chains.•There are many technical and methodological challenges.•Major research opportunities in conceptual modelling and validation.•This paper presents a life-cycle based framework to guide modellers and authors. Hybrid simulation (defined as a modelling approach that combines two or more of the following methods: discrete-event simulation, system dynamics, and agent-based simulation) has experienced near-exponential growth in popularity in the past two decades. However, a large proportion of the academic literature on hybrid simulation is found in computer science and engineering journals. Given the importance of this emerging area and its relevance to operational research, this paper provides a review of the topic from an OR perspective. The results of a review of the hybrid simulation literature are presented, using a novel framework based on the simulation lifecycle that will be useful for future modellers and authors alike. Promising areas for future research are identified: these include the development of new methods for conceptual modelling and for model validation. Currently the main application areas are healthcare, supply chain management and manufacturing, and the majority of published models combine discrete-event simulation and system dynamics.