Résumé
The debate over the role of stochasticity is central in evolutionary biology, often summarised by whether or not evolution is predictable or repeatable. Here we distinguish three types of stochasticity: stochasticity of mutation and variation, of individual life histories and of environmental change. We then explain when stochasticity matters in evolution, distinguishing four broad situations: stochasticity contributes to maladaptation or limits adaptation; it drives evolution on flat fitness landscapes (evolutionary freedom); it might promote jumps from one fitness peak to another (evolutionary revolutions); and it might shape the selection pressures themselves. We show that stochasticity, by directly steering evolution, has become an essential ingredient of evolutionary theory beyond the classical Wright-Fisher or neutralist-selectionist debates.