The neural crest (NC) is a multipotent cell population in vertebrate embryos with extraordinary migratory capacity. The NC is crucial for vertebrate development and forms a myriad of cell derivatives throughout the body, including pigment cells, neuronal cells of the peripheral nervous system, cardiomyocytes and skeletogenic cells in craniofacial tissue. NC induction occurs at the end of gastrulation when the multipotent population of NC progenitors emerges in the ectodermal germ layer in the neural plate border region. In the process of NC fate specification, fate-specific markers are expressed in multipotent progenitors, which subsequently adopt a specific fate. Thus, NC cells delaminate from the neural plate border and migrate extensively throughout the embryo until they differentiate into various cell derivatives. Multiple signalling pathways regulate the processes of NC induction and specification. This review explores the ongoing role of the Wnt/β-catenin signalling pathway during NC development, focusing on research undertaken in the Teleost model organism, zebrafish (Danio rerio). We discuss the function of the Wnt/β-catenin signalling pathway in inducing the NC within the neural plate border and the specification of melanocytes from the NC. The current understanding of NC development suggests a continual role of Wnt/β-catenin signalling in activating and maintaining the gene regulatory network during NC induction and pigment cell specification. We relate this to emerging models and hypotheses on NC fate restriction. Finally, we highlight the ongoing challenges facing NC research, current gaps in knowledge, and this field’s potential future directions.