Prospective approaches for large-scale greenhouse gas removal (GGR) are now central to the post 2015 international commitment to limit global temperature rise to below 1.5 oC. However, the feasibility of large-scale GGR has been repeatedly questioned, with most systematic analyses focusing only on the physical, technical and economic challenges of deploying it at scale. But social and political dimensions will be just as, if not more, important to how possible futures play out. In this paper we present one of the first reviews of the international peer-reviewed literature pertaining to the social and political dimensions of large-scale GGR, with a specific focus on two predominant approaches: biomass energy with carbon capture and storage (BECCS) and afforestation / reforestation (AR). Our analysis of 78 studies reveals two important insights. First, it identifies six key social and political dimensions of GGR feasibility, namely: economics and incentives; innovation; societal engagement; governance, regulation and politics; complexity and uncertainty; ethics, equity and justice. Second, our review reveals three contested ways in which BECCS and AR and their feasibility are being framed in the literature: (i) a techno-economic framing; (ii) a social and political acceptability framing; and (iii) a responsible development framing. While the first two are already predominant in the literature, the third will, and indeed should, become increasingly pertinent. Understanding the third requires new ways of mapping and accounting for the social and political dimensions of feasibility if the assessment, innovation and governance of GGR in relation to alternative climate futures is to be responsibly undertaken.