The neural crest shows an astonishing multipotency, generating multiple neural derivatives, but also pigment cells, skeletogenic and other cell types. The question of how this process is controlled has been the subject of an ongoing debate for more than 35 years. Based upon new observations of zebrafish pigment cell development, we have recently proposed a novel, dynamic model that we believe goes some way to resolving the controversy. Here, we will firstly summarize the traditional models and the conflicts between them, before outlining our novel model. We will also examine our recent dynamic modelling studies, looking at how these reveal behaviors compatible with the biology proposed. We will then outline some of the implications of our model, looking at how it might modify our views of the processes of fate specification, differentiation, and commitment.