A vast majority of heat exchangers suffer from unwanted deposition of material on the surface, which severely inhibits their performance and thus marks one of the biggest challenges in heat transfer. Despite numerous scientific investigations, prediction and prevention of fouling remain unresolved issues in process engineering and are responsible for large economic losses and environmental damage. This review article focuses specifically on crystallization fouling, providing a comprehensive overview of the state-of-the-art of fouling in heat exchangers. The fundamentals of the topic are discussed, as the term fouling resistance is introduced along with distinct fouling behaviour, observed in laboratory and industrial environments. Insight into subsequent phases of the fouling process is provided, along with the accompanying microscale events. Furthermore, the effects of fluid composition, temperature, flow velocity, surface condition, nucleate boiling and composite fouling are comprehensively discussed. Fouling modelling is systematically reviewed, from the early work of Kern and Seaton to recently used artificial neural networks and computational fluid dynamics. Finally, the most common fouling mitigation approaches are presented, including design considerations and various on-line strategies, as well as off-line cleaning. According to our review, several topics require further study, such as the initial stage of crystal formation, the effects of ageing, the interplay of two or more fouling mechanisms and the underlying phenomena of several mitigation strategies.