Neurocristopathies (NCPs) encompass a spectrum of disorders arising from issues during the formation and migration of neural crest cells (NCCs). NCCs undergo epithelial–mesenchymal transition (EMT) and upon key developmental gene deregulation, fetuses and neonates are prone to exhibit diverse manifestations depending on the affected area. These conditions are generally rare and often have a genetic basis, with many following Mendelian inheritance patterns, thus making them perfect candidates for precision medicine. Examples include cranial NCPs, like Goldenhar syndrome and Axenfeld–Rieger syndrome; cardiac–vagal NCPs, such as DiGeorge syndrome; truncal NCPs, like congenital central hypoventilation syndrome and Waardenburg syndrome; and enteric NCPs, such as Hirschsprung disease. Additionally, NCCs’ migratory and differentiating nature makes their derivatives prone to tumors, with various cancer types categorized based on their NCC origin. Representative examples include schwannomas and pheochromocytomas. This review summarizes current knowledge of diseases arising from defects in NCCs’ specification and highlights the potential of precision medicine to remedy a clinical phenotype by targeting the genotype, particularly important given that those affected are primarily infants and young children.