Environmental stressors alter relationships between physiology and behaviour

•Stressors amplify physiological and behavioural links by increasing variation.•Stressors can attenuate such relationships by decreasing variation.•These mechanisms stem from differing sensitivity to stressors among phenotypes.•These influences underlie a range of ecological phenomena.•They could also be important for evolutionary responses to environmental change. Although correlations have frequently been observed between specific physiological and behavioural traits across a range of animal taxa, the nature of these associations has been shown to vary. Here we argue that a major source of this inconsistency is the influence of environmental stressors, which seem capable of revealing, masking, or modulating covariation in physiological and behavioural traits. These effects appear to be mediated by changes in the observed variation of traits and differential sensitivity to stressors among phenotypes. Considering that wild animals routinely face a range of biotic and abiotic stressors, increased knowledge of these effects is imperative for understanding the causal mechanisms of a range of ecological phenomena and evolutionary responses to stressors associated with environmental change.