Few situations in life are completely novel. We effortlessly generalise prior knowledge to solve novel problems, abstracting common structure and mapping it onto new sensorimotor specifics. Here we trained mice on a series of reversal learning problems that shared the same structure but had different physical implementations. Performance improved across problems, demonstrating transfer of knowledge. Neurons in medial prefrontal cortex (mPFC) maintained similar representations across multiple problems, despite their different sensorimotor correlates, whereas hippocampal (dCA1) representations were more strongly influenced by the specifics of each problem. Critically, this was true both for representations of the events that comprised each trial, and those that integrated choices and outcomes over multiple trials to guide subjects’ decisions. These data suggest that PFC and hippocampus play complementary roles in generalisation of knowledge, with the former abstracting the common structure among related problems, and the latter mapping this structure onto the specifics of the current situation.