Centromeres, chromosomal regions that become physically linked to the spindle during cell division, ensure equal division of genetic material between daughter cells. They are ubiquitous and essential in eukaryotic life. In this primer, we ask the questions 'What defines a functional centromere?' and 'What do all centromeres have in common?' To address these questions we highlight what is known about centromere size, centromere architecture, underlying DNA sequence and centromeric proteins. Studies from a variety of organisms reveal a vast diversity in centromere form and function that remains perplexing and largely unexplained.