Open Science holds the promise to make scientific endeavours more inclusive, participatory, understandable, accessible and re-usable for large audiences. However, making processes open will not per se drive wide reuse or participation unless also accompanied by the capacity (in terms of knowledge, skills, financial resources, technological readiness and motivation) to do so. These capacities vary considerably across regions, institutions and demographics. Those advantaged by such factors will remain potentially privileged, putting Open Science's agenda of inclusivity at risk of propagating conditions of ‘cumulative advantage’. With this paper, we systematically scope existing research addressing the question: ‘What evidence and discourse exists in the literature about the ways in which dynamics and structures of inequality could persist or be exacerbated in the transition to Open Science, across disciplines, regions and demographics?’ Aiming to synthesize findings, identify gaps in the literature and inform future research and policy, our results identify threats to equity associated with all aspects of Open Science, including Open Access, Open and FAIR Data, Open Methods, Open Evaluation, Citizen Science, as well as its interfaces with society, industry and policy. Key threats include: stratifications of publishing due to the exclusionary nature of the author-pays model of Open Access; potential widening of the digital divide due to the infrastructure-dependent, highly situated nature of open data practices; risks of diminishing qualitative methodologies as ‘reproducibility’ becomes synonymous with quality; new risks of bias and exclusion in means of transparent evaluation; and crucial asymmetries in the Open Science relationships with industry and the public, which privileges the former and fails to fully include the latter.