Executive function is commonly assessed by assays of cognitive flexibility such as reversal learning and attentional set-shifting. Disrupted performance in these assays, apparent in many neuropsychiatric disorders, is frequently interpreted as inability to overcome prior associations with reward. However, non-rewarded or irrelevant associations may be of considerable importance in both discrimination learning and cognitive flexibility. Non-rewarded associations can have greater influence on choice behaviour than rewarded associations in discrimination learning. Pathology-related deficits in cognitive flexibility can produce selective disruptions to both the processing of irrelevant associations and associations with reward. Genetic and pharmacological animal models demonstrate that modulation of reversal learning may result from alterations in either rewarded or non-rewarded associations. Successful performance in assays of cognitive flexibility can therefore depend on a combination of rewarded, non-rewarded, and irrelevant associations derived from previous learning, accounting for some inconsistencies observed in the literature. Taking this combination into account may increase the validity of animal models and may also reveal pathology-specific differences in problem solving and executive function.