Recently, major progress has been made to develop computational models to predict and explain the mechanisms and behaviors of gene regulation. Here, we review progress on how these mechanisms and behaviors have been interpreted with analog models, where cell properties continuously modulate transcription, and digital models, where gene modulation involves discrete activation and inactivation events. We introduce recent experimental approaches, which measure these gene regulatory behaviors at single-cell and single-molecule resolution, and we discuss the integration of these approaches with computational models to reveal biophysical insight. By analyzing simple toy models in the context of existing experimental capabilities, we discuss the interplay between different experiments and different models to measure and interpret gene regulatory behaviors. Finally, we review recent successes in the development of predictive computational models for the control of gene regulation behaviors.