With the exception of a few model species, individual differences in cognition remain relatively unstudied in non-human animals. One intriguing possibility is that variation in cognition is functionally related to variation in personality. Here, we review some examples and present hypotheses on relationships between personality (or behavioural syndromes) and individual differences in cognitive style. Our hypotheses are based largely on a connection between fast-slow behavioural types (BTs; e.g. boldness, aggressiveness, exploration tendency) and cognitive speed -accuracy trade-offs. We also discuss connections between BTs, cognition and ecologically important aspects of decision-making, including sampling, impulsivity, risk sensitivity and choosiness. Finally, we introduce the notion of cognition syndromes, and apply ideas from theories on adaptive behavioural syndromes to generate predictions on cognition syndromes.