Neural crest cells are central to vertebrate development and evolution, endowing vertebrates with a "new head" that resulted in morphological, physiological, and behavioral features that allowed vertebrates to become active predators. One remarkable feature of neural crest cells is their multi-germ layer potential that allows for the formation of both ectodermal (pigmentation, peripheral glia, sensory neurons) and mesenchymal (connective tissue, cartilage/bone, dermis) cell types. Understanding the cellular and evolutionary origins of this broad cellular potential in the neural crest has been a long-standing focus for developmental biologists. Here, we review recent work that has demonstrated that neural crest cells share key features with pluripotent blastula stem cells, including expression of the Yamanaka stem cell factors (Oct3/4, Klf4, Sox2, c-Myc). These shared features suggest that pluripotency is either retained in the neural crest from blastula stages or subsequently reactivated as the neural crest forms. We highlight the cellular and molecular parallels between blastula stem cells and neural crest cells and discuss the work that has led to current models for the cellular origins of broad potential in the crest. Finally, we explore how these themes can provide new insights into how and when neural crest cells and pluripotency evolved in vertebrates and the evolutionary relationship between these populations.