Interactions between frontal cortex and basal ganglia are instrumental in supporting motivated control over action and learning. Computational models have been proposed at multiple levels of description, from biophysics up to algorithmic approaches. I will describe recent attempts to link across levels of description to develop on the one hand, mechanistic neural models with sufficient detail to make predictions about electrophysiology, pharmacology and genetic manipulations, and on the other hand, higher level computational descriptions which often have normative interpretations and, pragmatically, are more suited to quantitatively fit behavioral data. By fitting outputs of neural models with reduced versions, one can derive predictions about how parametric variation of particular neural mechanisms should give rise to observable change in latent computational parameters -- even if the two levels are not perfectly isomorphic. Examples include the impact of dopamine on learning and choice incentive, prefrontal-subthalamic modulation of decision thresholds, and hierarchical control over actions across multiple corticostriatal circuits. In each case, the (optimistic) result is a better understanding of the domain than that afforded by either level of model alone.