In this perspective article, we call for more engagement with the unexplored politics of residual emissions. Residual emissions are those emissions that remain at the point of net zero, despite abatement efforts. Unlike carbon dioxide removal, which has been the focus of a lively research and policy debate, the notion of residual emissions remains relatively unexplored so far. With the mainstreaming of net zero as the long-term goal of climate policy, the politics of residual emissions are set to become a key point of contestation. Claims about residual emissions tend to revolve around notions of necessity and possibility, i.e. emissions that derive from activities deemed socially necessary yet impossible to fully abate. In this perspective article, we highlight how such claims are socially constructed and ultimately contingent on values, norms and interests. We call upon researchers to help render visible the geographically and historically contingent claims to necessity and possibility that underpin projected residual emissions. We see this as an important means to repoliticize debates about the limits and possibilities of emissions abatement, and suggest entry points for such research efforts.