Studies of the evolution of helping have traditionally used the explanatory frameworks of reciprocity and altruism towards relatives, but recently there has been an increasing interest in other kinds of explanations. We review the success or otherwise of work investigating alternative processes and mechanisms, most of which fall under the heading of cooperation for direct benefits. We evaluate to what extent concepts such as by-product benefits, pseudo-reciprocity, sanctions and partner choice, markets and the build-up of cross-species spatial trait correlations have contributed to the study of the evolution of cooperation. We conclude that these alternative ideas are successful and show potential to further increase our understanding of cooperation. We also bring up the origin and role of common interest in the evolution of cooperation, including the appearance of organisms. We note that there are still unresolved questions about the main processes contributing to the evolution of common interest. Commenting on the broader significance of the recent developments, we argue that they represent a justified balancing of the importance given to different major hypotheses for the evolution of cooperation. This balancing is beneficial because it widens considerably the range of phenomena addressed and, crucially, encourages empirical testing of important theoretical alternatives.