Purpose The purpose of this paper is to systematically review and assess the current status of research on supply chain sustainability from a network structural perspective and provide an organising framework for future scholarship in this area. Design/methodology/approach By adopting an evidence-based approach, this study conducts a systematic review of 73 articles from 18 peer-reviewed journals published between 2000 and 2020. Findings Adopting a social network analysis approach, the review identifies specific node-level (i.e. degree centrality, closeness centrality and betweenness centrality) and network-level (i.e. network density, network sub-groups and network diversity) structural properties that play a role in supply chain sustainability. The results reveal that structural properties determine the extent of perception of sustainability risks, the diffusion of sustainability targets, introduction of sustainable innovations, development of sustainability capabilities, adoption of sustainability initiatives and the monitoring of sustainability performance throughout the supply chain. Originality/value By distinguishing between supply network and sustainable supply network types, this study extends the existing understandings of the role of network connectivity patterns in supply chain sustainability through synthesising and evaluating the extant literature. This study further clarifies the role of these network structural properties in supply chain sustainability by describing their impact on a set of sustainable supply chain management practices through which firms achieve sustainability goals across their supply chains.