We provide selected examples from the fish literature of phenomena found in fish that are currently being examined in discussions of cognitive abilities and evolution of neocortex size in primates. In the context of social intelligence, we looked at living in individualised groups and corresponding social strategies, social learning and tradition, and co-operative hunting. Regarding environmental intelligence, we searched for examples concerning special foraging skills, tool use, cognitive maps, memory, anti-predator behaviour, and the manipulation of the environment. Most phenomena of interest for primatologists are found in fish as well. We therefore conclude that more detailed studies on decision rules and mechanisms are necessary to test for differences between the cognitive abilities of primates and other taxa. Cognitive research can benefit from future fish studies in three ways: first, as fish are highly variable in their ecology, they can be used to determine the specific ecological factors that select for the evolution of specific cognitive abilities. Second, for the same reason they can be used to investigate the link between cognitive abilities and the enlargement of specific brain areas. Third, decision rules used by fish could be used as 'null-hypotheses' for primatologists looking at how monkeys might make their decisions. Finally, we propose a variety of fish species that we think are most promising as study objects.