In the last few years, the role of non-coding regulatory elements and their involvement in human disease have received great attention. Among the non-coding regulatory sequences, enhancers are particularly important for the proper establishment of cell type-specific gene-expression programs. Furthermore, the disruption of enhancers can lead to human disease through two main mechanisms: (i) Mutations or copy number variants can directly alter the enhancer sequences and thereby affect expression of their target genes; (ii) structural variants can provoke changes in 3-D chromatin organization that alter neither the enhancers nor their target genes, but rather the physical communication between them. In this review, these pathomechanisms are mostly discussed in the context of neurocristopathies, congenital disorders caused by defects that occur during neural crest development. We highlight why, due to its contribution to multiple tissues and organs, the neural crest represents an important, yet understudied, cell type involved in multiple congenital disorders. Moreover, we discuss currently available resources and experimental models for the study of human neurocristopathies. Last, we provide some practical guidelines that can be followed when investigating human neurocristopathies caused by structural variants. Importantly, these guidelines can be useful not only to uncover the etiology of human neurocristopathies, but also of other human congenital disorders in which enhancer disruption is involved.