Individual animals routinely face decisions that are crucial to their fitness. In social species, however, many of these decisions need to be made jointly with other group members because the group will split apart unless a consensus is reached. Here, we review empirical and theoretical studies of consensus decision making, and place them in a coherent framework. In particular, we classify consensus decisions according to the degree to which they involve conflict of interest between group members, and whether they involve either local or global communication; we ask, for different categories of consensus decision, who makes the decision, what are the underlying mechanisms, and what are the functional consequences. We conclude that consensus decision making is common in non-human animals, and that cooperation between group members in the decision-making process is likely to be the norm, even when the decision involves significant conflict of interest.