Endogenous chromosomes contain centromeres to direct equal chromosomal segregation in mitosis and meiosis. The location and function of existing centromeres is usually maintained through cell cycles and generations. Recent studies have investigated how the centromere-specific histone H3 variant CENP-A is assembled and replenished after DNA replication to epigenetically propagate the centromere identity. However, existing centromeres occasionally become inactivated, with or without change in underlying DNA sequences, or lost after chromosomal rearrangements, resulting in acentric chromosomes. New centromeres, known as neocentromeres, may form on ectopic, non-centromeric chromosomal regions to rescue acentric chromosomes from being lost, or form dicentric chromosomes if the original centromere is still active. In addition, de novo centromeres can form after chromatinization of purified DNA that is exogenously introduced into cells. Here, we review the phenomena of naturally occurring and experimentally induced new centromeres and summarize the genetic (DNA sequence) and epigenetic features of these new centromeres. We compare the characteristics of new and native centromeres to understand whether there are different requirements for centromere establishment and propagation. Based on our understanding of the mechanisms of new centromere formation, we discuss the perspectives of developing more stably segregating human artificial chromosomes to facilitate gene delivery in therapeutics and research. [ABSTRACT FROM AUTHOR]