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There is an explosion of interest in the therapeutic potential of non-invasive brain stimulation (NIBS) for neurological and psychiatric disorders. A common target is to try and augment intact or impaired cognitive function, or potentiate some form of behavioural therapy.  Despite these cognitive goals, most work in this field is physiological. The aim is to identify neural factors that mediate (variable) NIBS effects. There is a striking absence of psychological models of how the target behaviour is generated in the first place. This is a critical explanatory gap. I will present some of our recent work on sensorimotor adaptation to illustrate the explanatory value of a model-based approach. Our information processing model accounted for ~99% of participants' baseline behavioural variation. A single parameter within the model enabled us to identify neurochemical, functional and white matter structural connectivity correlates of the target function. To test a causal hypothesis about how targeted stimulation changes behaviour, we stimulated sensorimotor cortex. As predicted, across individuals, NIBS induced co-varying change in neurochemistry, computation and behaviour. Thus the model enabled us to generate a mechanistic explanatory account of how sensorimotor memories are formed, retained and potentiated via NIBS. We propose increased use of models to understand mechanism, explain variation, and advance NIBS therapeutics towards individually tailored interventions.