Supply networks emerge as companies procure goods from one another to produce their own products. Due to a chronic lack of data, studies on these emergent structures have long focussed on local neighbourhoods, assuming simple, chain-like structures. However, studies conducted since 2001 have shown that supply chains are indeed complex networks that exhibit similar organisational patterns to other network types. In this paper, we present a critical review of theoretical and model based studies which conceptualise supply chains from a network science perspective, showing that empirical data do not always support theoretical models that were developed, and argue that different industrial settings may present different characteristics. Consequently, a need that arises is the development and reconciliation of interpretation across different supply network layers such as contractual relations, material flow, financial links, and co-patenting, as these different projections tend to remain in disciplinary siloes. Other gaps include a lack of null models that show whether the observed properties are meaningful, a lack of dynamical models that can inform how layers evolve and adopt to changes, and a lack of studies that investigate how local decisions enable emergent outcomes. We conclude by asking the network science community to help bridge these gaps by engaging with this important area of research.