Collective behaviour is widespread in the animal kingdom and can enhance individual fitness. Yet not all collective behaviours are adaptations. Instead, some may be nonadaptive or 'evolutionary spandrels'-traits that originated as by-products in the sense proposed by Stephen Jay Gould and Richard Lewontin. Here, we argue that self-organising processes provide a route through which evolutionary spandrels in collective animal behaviour can occur, and we provide three examples: spatial organisation in primate groups, division of labour in ants, and insect chorusing. We then consider how such outcomes may be co-opted into adaptive roles through exaptation and conclude by outlining the challenges associated with testing adaptive and nonadaptive hypotheses in collective behaviour research using individual-based studies, phylogenetic comparative analyses, and agent-based models.