Abstract: Besides focusing on the adaptive significance of collective movements, it is crucial to study the mechanisms and dynamics of decision-making processes at the individual level underlying the higher-scale collective movements. It is now commonly admitted that collective decisions emerge from interactions between individuals, but how individual decisions are taken, i.e. how far they are modulated by the behaviour of other group members, is an under-investigated question. Classically, collective movements are viewed as the outcome of one individual's initiation (the leader) for departure, by which all or some of the other group members abide. Individuals assuming leadership have often been considered to hold a specific social status. This hierarchical or centralized control model has been challenged by recent theoretical and experimental findings, suggesting that leadership can be more distributed. Moreover, self-organized processes can account for collective movements in many different species, even in those that are characterized by high cognitive complexity. In this review, we point out that decision-making for moving collectively can be reached by a combination of different rules, i.e. individualized (based on inter-individual differences in physiology, energetic state, social status, etc.) and self-organized (based on simple response) ones for any species, context and group size.