In 1994 and 1996, Andreas Wagner introduced a novel model in two papers addressing the evolution of genetic regulatory networks. This work, and a suite of papers that followed using similar models, helped integrate network thinking into biology and motivate research focused on the evolution of genetic networks. The Wagner network has its mathematical roots in the Ising model, a statistical physics model describing the activity of atoms on a lattice, and in neural networks. These models have given rise to two branches of applications, one in physics and biology and one in artificial intelligence and machine learning. Here, we review development along these branches, outline similarities and differences between biological models of genetic regulatory circuits and neural circuits models used in machine learning, and identify ways in which these models can provide novel insights into biological systems. J. Exp. Zool. (Mol. Dev. Evol.) 324B: 1–12, 2015. © 2014 Wiley Periodicals, Inc.