Engineering complex genetic functions in mammalian cells will require predictive models of gene regulation. Since gene expression is stochastic, leading to cell-to-cell heterogeneity, these models depend on single-cell measurements. Here, we summarize recent microscopy and sequencing-based single-cell measurements of transcription and its chromatin-based regulation. Then, we describe synthetic biology methods for manipulating chromatin, and highlight how they could be coupled to single-cell measurements. We discuss theoretical models that connect some chromatin inputs to transcriptional outputs. Finally, we point out the connections between the models that would allow us to integrate them into one global input-output gene regulatory function.