Peer review is a pillar of the scientific system, serving as a pre-publication quality assurance mechanism. Active peer reviewers hold power over which ideas and approaches enter the scientific discourse. They are simultaneously burdened with unpaid labour, as peer reviewing is generally only incentivized by the notion of contributing to the public scientific good. The present large-scale mixed-methods global study (n = 3677 social scientists from 49 countries) investigates the power, burden, and perceptions of peer reviewing in terms of academic prestige, geography, gender identity, academic legacy, and structural marginalisation. We find a clear bias favouring reviewers in and from academically prestigious countries. Men reviewed slightly more than others, and marginalized researchers felt they were investing more time and effort in their reviews than others. Exploratory analyses of reasons for rejecting review requests and spontaneous associations with peer review add to a nuanced picture of how differences in academic prestige shape the peer review landscape. We discuss underlying mechanisms and potential implications for improving peer review processes.