Neocentromeres are ectopic sites where new functional kinetochores assemble and permit chromosome segregation. Neocentromeres usually form following genomic alterations that remove or disrupt centromere function. The ability to form neocentromeres is conserved in eukaryotes ranging from fungi to mammals. Neocentromeres that rescue chromosome fragments in cells with gross chromosomal rearrangements are found in several types of human cancers, and in patients with developmental disabilities. In this review, we discuss the importance of neocentromeres to human health and evaluate recently developed model systems to study neocentromere formation, maintenance, and function in chromosome segregation. Additionally, studies of neocentromeres provide insight into native centromeres; analysis of neocentromeres found in human clinical samples and induced in model organisms distinguishes features of centromeres that are dependent on centromere DNA from features that are epigenetically inherited together with the formation of a functional kinetochore.