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Aim The negative correlation between temperature and body size of ectothermic animals (broadly known as the temperature-size rule or TSR) is a widely observed pattern, especially in aquatic organisms. Studies have claimed that the TSR arises due to decreased oxygen solubility and increasing metabolic costs at warmer temperatures, whereby oxygen supply to a large body becomes increasingly difficult. However, mixed empirical evidence has led to a controversy about the mechanisms affecting species' size and performance under different temperatures. We review the main competing genetic, physiological and ecological explanations for the TSR and suggest a roadmap to move the field forward. Location Global. Taxa Aquatic ectotherms. Time period 1980-present. Results We show that current studies cannot discriminate among alternative hypotheses and none of the hypotheses can explain all TSR-related observations. To resolve this impasse, we need experiments and field-sampling programmes that specifically compare alternative mechanisms and formally consider energetics related to growth costs, oxygen supply and behaviour. We highlight the distinction between evolutionary and plastic mechanisms, and suggest that the oxygen limitation debate should separate processes operating on short, decadal and millennial time-scales. Conclusions Despite decades of research, we remain uncertain whether the TSR is an adaptive response to temperature-related physiological (enzyme activity) or ecological changes (food, predation and other mortality), or a response to constraints operating at a cellular level (oxygen supply and associated costs). To make progress, ecologists, physiologists, modellers and geneticists should work together to develop a cross-disciplinary research programme that integrates theory and data, explores time-scales over which the TSR operates, and assesses limits to adaptation or plasticity. We identify four questions for such a programme. Answering these questions is crucial given the widespread impacts of climate change and reliance of management on models that are highly dependent on accurate representation of ecological and physiological responses to temperature.