Аннотация:Summary Recent progress has been made on the study of personality in animals, both from a mechanistic and a functional perspective. While we start knowing more about the proximal mechanisms responsible for the consistent differences in behaviour between individuals in a population, little is known yet about the relationship between the phenotypic distribution of personality traits, or combinations of traits, and fitness. Here we provide an overview of the available literature on the fitness consequences of personality traits in natural populations. We start by a description of two case studies that have examined the role of natural selection on personality traits in the wild (i.e., the great tit, Parus major and bighorn sheep, Ovis canadensis), and review other studies that have reported some links between personality traits and fitness indices, in a large variety of animal species. We continue by outlining both direct approaches (i.e., measuring correlational selection on personality trait combinations) and indirect approaches (i.e., comparing correlations between personality traits within and between populations) to study suites of correlated traits from an adaptive perspective. This review, we hope, will be able to stimulate the use of the phenotypic selection analysis applied to the study of selection on personality traits in animals.