•Computational psychiatry holds promise for mechanistic discovery in addiction.•This approach captures latent factors driving behavioral differences from health.•Emerging support also for capturing variation defining addiction cycles and states.•Research needs to better account for the heterogeneous, dynamic nature of addiction.•Expanding the parameter space examined and duration of observation will be key. Computational psychiatry provides a powerful new approach for linking the behavioral manifestations of addiction to their precise cognitive and neurobiological substrates. However, this emerging area of research is still limited in important ways. While research has identified features of reinforcement learning and decision-making in substance users that differ from health, less emphasis has been placed on capturing addiction cycles/states dynamically, within-person. In addition, the focus on few behavioral variables at a time has precluded more detailed consideration of related processes and heterogeneous clinical profiles. We propose that a longitudinal and multidimensional examination of value-based processes, a type of dynamic ‘computational fingerprint’, will provide a more complete understanding of addiction as well as aid in developing better tailored and timed interventions.