The gut is enmeshed by a number of cellular networks, but there is only a limited understanding of how these networks generate the complex patterns of activity that drive gut contractile functions. Here we review two fundamental types of cell behaviour, excitable and oscillating, and the patterns that networks of such cells generate, trigger waves and phase waves, respectively. We use both the language of biophysics and the theory of nonlinear dynamics to define these behaviours and understand how they generate patterns. Based on this we look for evidence of trigger and phase waves in the gut, including some of our recent work on the small intestine.