Stem cells exist in vitro in a spectrum of interconvertible pluripotent states. Analyzing hundreds of hiPSCs derived from different individuals, we show the proportions of these pluripotent states vary considerably across lines. We discover 13 gene network modules (GNMs) and 13 regulatory network modules (RNMs), which are highly correlated with each other suggesting that the coordinated co-accessibility of regulatory elements in the RNMs likely underlie the coordinated expression of genes in the GNMs. Epigenetic analyses reveal that regulatory networks underlying self-renewal and pluripotency are more complex than previously realized. Genetic analyses identify thousands of regulatory variants that overlapped predicted transcription factor binding sites and are associated with chromatin accessibility in the hiPSCs. We show that the master regulator of pluripotency, the NANOG-OCT4 Complex, and its associated network are significantly enriched for regulatory variants with large effects, suggesting that they play a role in the varying cellular proportions of pluripotency states between hiPSCs. Our work bins tens of thousands of regulatory elements in hiPSCs into discrete regulatory networks, shows that pluripotency and self-renewal processes have a surprising level of regulatory complexity, and suggests that genetic factors may contribute to cell state transitions in human iPSC lines.