Developmental processes are carefully orchestrated. A multi-cellular organism can only emerge from a single fertilised egg cell because gene expression is robustly regulated in space and time by networks of transcriptional regulators. Single cell transcriptomic data allow us to probe and map these networks in unprecedented detail. Here we develop an information theoretical framework to infer candidate gene (co-)regulatory networks and distill mechanistic hypotheses from single cell data. Information theory offers clear advantages for such data, where cell-to-cell variability is all pervasive and sample sizes are large. Higher-order information theoretical functionals capture interactions and dependencies between genes reliably in both in silico and real data.