<p>Computational policy modelling appeals to policymakers seeking to understand potential outcomes of policy decisions, yet there are long-standing concerns about the “social robustness” of the knowledge it generates. A key route to socially robust policy modelling is the active involvement of publics as partners, and not only subjects, of modelling; yet the technical and abstracted nature of the modelling process poses particular challenges for conventional involvement practice. This scoping review of published computational modelling papers which report public involvement explores both practical elements of involvement in modelling and the tacit or explicit justifications authors offer for involving publics. We found a preponderance of professional stakeholders over “lay” publics and a bifurcation between informal feedback and highly structured input. We conclude that approaches to public involvement in computational policy modelling should seek ongoing dialogic involvement across the stages of the modelling process, be more attentive to power dynamics in the involvement process, and consider how involvement can be inclusive of diverse publics.</p>