The enteric nervous system modulates intestinal behaviours such as motor patterns and secretion. While much is known about different types of neurons and simple reflexes in the intestine, it remains unclear how complex behaviours are generated. Mathematical modelling is an important tool for assisting the understanding of how the neurons and reflexes can be pieced together to generate intestinal behaviours.Models have identified a functional role for slow excitatory post synaptic potentials (EPSPs) by distinguished between fast and slow EPSPs in the ascending excitation reflex. These models also discovered coordinated firing of similarly located neurons as emergent properties of feedforward networks of interneurons in the intestine.A model of the recurrent network of intrinsic sensory neurons identified important control mechanisms to prevent uncontrolled firing due to positive feedback and that the interaction between these control mechanisms and slow EPSPs is necessary for the networks to encode ongoing sensory stimuli. This model also showed that such networks may mediate migrating motor complexes.A network model of VIP neurons in the submucosal plexus found this relatively sparse recurrent network could produce uncontrolled firing under conditions that appear to be related to cholera toxin induced hypersecretion.Abstract modelling of the intestinal fed‐state motor patterns has identified how stationary contractions can arise from a polarised network. These models have also helped predict and explained pharmacological evidence for two rhythm generators and the requirement of feedback from contractions in the circular muscle. This article is protected by copyright. All rights reserved.