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Abstract Compensatory growth (CG) is a phase of accelerated growth when favourable conditions are restored after a period of growth depression. CG reduces variance in size by causing growth trajectories to converge and is important to fisheries management, aquaculture and life history analysis because it can offset the effects of growth arrests. Compensatory growth has been demonstrated in both individually housed and grouped fish, typically after growth depression has been induced by complete or partial food deprivation. Partial, full and over‐compensation have all been evoked in fish, although over‐compensation has only been demonstrated when cycles of deprivation and satiation feeding have been imposed. Individually housed fish have shown that CG is partly a response to hyperphagia when rates of food consumption are significantly higher than those in fish that have not experienced growth depression. The severity of the growth depression increases the duration of the hyperphagic phase rather than maximum daily feeding rate. In many studies, growth efficiencies were higher during CG. Changes in metabolic rate and swimming activity have not been demonstrated yet to play a role. Periods of food deprivation induce changes in the storage reserves, particularly lipids, of fish. Apart from the strong evidence for the restoration of somatic growth trajectories, CG is a response to restore lipid levels. Although several neuro‐peptides, including neuropeptide‐Y, are probably involved in the control of appetite, their role and the role of hormones, such as growth hormone (GH) and insulin‐like growth factor (IGF), in the hyperphagia associated with CG are still unclear. The advantages of CG probably relate to size dependencies of mortality, fecundity and diet that are characteristic of teleosts. These size dependencies favour a recovery from the effects of growth depression if environmental factors allow. High growth rates may also impose costs, including adverse effects on future development, growth, reproduction and swimming performance. Hyperphagia may lead to riskier behaviour in the presence of predators. CG's evolutionary consequences are largely unexplored. An understanding of why animals grow at rates below their physiological capacity, an evaluation of the costs of rapid growth and the identification of the constraints on growth trajectories represent major challenges for life‐history theory.