Nowadays, reactor runaway is still a crucial phenomen from the safety viewpoint. About 120 scientific journal articles are published every year in the last decade in which thermal runaway is a keyword. The possible cause and consequences of reactor runaway are adressed where the worst case is the explosion of the reactor. Prevention steps to avoid the development of thermal runaway include the appropriate design of the reactor, the operation strategy and an early warning detection system. The available assessment methods for thermal risk analysis are addressed in detail. Reactor runaway criteria can indicate early the thermal runaway, which criteria are addressed in this review in detail under three classes: geometry-, sensitivity-, and stability-based runaway criteria. Operation strategy of semi-batch reactors can be designed by calculating Westerterp-diagram whose evolution is cleary presented. Significant works on the field of the reactor design, operation and reactor safety are collected and evaluated. Finally possible further research areas are suggested to improve our knowledge about thermal safety, such as investigating parameter uncertainty in runaway indication or optimize the safety actions to moderate the consequences of runaway. (C) 2020 The Author(s). Published by Elsevier B.V. on behalf of Institution of Chemical Engineers.