In many industries and processes, heat exchangers are of vital importance as they are used to transfer heat from one fluid to another. These fluids can be corrosive to heat exchangers, which are usually made of metallic materials. This paper illustrates that corrosion is an important problem in the operation of heat exchangers in many environments, for which no straightforward answer exists. Corrosion failures of heat exchangers are common, and corrosion often involves high maintenance or repair costs. In this review, an overview is given of what is known on corrosion in heat exchangers. The different types of corrosion encountered in heat exchangers and the susceptible places in the devices are discussed first. This is combined with an overview of failure analyses for each type of corrosion. Next, the effect of heat transfer on corrosion and the influence of corrosion on the thermohydraulic performances are discussed. Finally, the prevention and control of corrosion is tackled. Prevention goes from general design considerations and operation guidelines to the use of cathodic and anodic protection.