We review morphogenesis of the enteric nervous system from migratory neural crest cells, and defects of this process such as Hirschsprung disease, centering on cell motility and assembly, and cell adhesion and extracellular matrix molecules, along with cell proliferation and growth factors. We then review continuum and agent-based (cellular automata) models with rules of cell movement and logistical proliferation. Both movement and proliferation at the individual cell level are modeled with stochastic components from which stereotyped outcomes emerge at the population level. These models reproduced the wave-like colonization of the intestine by enteric neural crest cells, and several new properties emerged, such as colonization by frontal expansion, which were later confirmed biologically. These models predict a surprising level of clonal heterogeneity both in terms of number and distribution of daughter cells. Biologically, migrating cells form stable chains made up of unstable cells, but this is not seen in the initial model. We outline additional rules for cell differentiation into neurons, axon extension, cell-axon and cell–cell adhesions, chemotaxis and repulsion which can reproduce chain migration. After the migration stage, the cells re-arrange as a network of ganglia. Changes in cell adhesion molecules parallel this, and we describe additional rules based on Steinberg's Differential Adhesion Hypothesis, reflecting changing levels of adhesion in neural crest cells and neurons. This was able to reproduce enteric ganglionation in a model. Mouse mutants with disturbances of enteric nervous system morphogenesis are discussed, and these suggest future refinement of the models. The modeling suggests a relatively simple set of cell behavioral rules could account for complex patterns of morphogenesis. The model has allowed the proposal that Hirschsprung disease is mostly an enteric neural crest cell proliferation defect, not a defect of cell migration. In addition, the model suggests an explanations for zonal and skip segment variants of Hirschsprung disease, and also gives a novel stochastic explanation for the observed discordancy of Hirschsprung disease in identical twins.