The centromere is a chromosomal structure that is essential for the accurate segregation of replicated eukaryotic chromosomes to daughter cells. In most centromeres, the underlying DNA is principally made up of repetitive DNA elements, such as tandemly repeated satellite DNA and retrotransposable elements. Paradoxically, for such an essential genomic region, the DNA is rapidly evolving both within and between species. In this review, we show that the centromere locus is a resilient structure that can undergo evolutionary cycles of birth, growth, maturity, death and resurrection. The birth phase is highlighted by examples in humans and other organisms where centromere DNA deletions or chromosome rearrangements can trigger the epigenetic assembly of neocentromeres onto genomic sites without typical features of centromere DNA. In addition, functional centromeres can be generated in the laboratory using various methodologies. Recent mapping of the foundation centromere mark, the histone H3 variant CENP-A, onto near-complete genomes has uncovered examples of new centromeres which have not accumulated centromere repeat DNA. During the growth period of the centromere, repeat DNA begins to appear at some, but not all, loci. The maturity stage is characterised by centromere repeat accumulation, expansions and contractions and the rapid evolution of the centromere DNA between chromosomes of the same species and between species. This stage provides inherent centromere stability, facilitated by repression of gene activity and meiotic recombination at and around the centromeres. Death to a centromere can result from genomic instability precipitating rearrangements, deletions, accumulation of mutations and the loss of essential centromere binding proteins. Surprisingly, ancestral centromeres can undergo resurrection either in the field or in the laboratory, via as yet poorly understood mechanisms. The underlying principle for the preservation of a centromeric evolutionary life cycle is to provide resilience and perpetuity for the all-important structure and function of the centromere.