Centromeres, and the kinetochores that assemble on them, are essential for accurate chromosome segregation. Diverse centromere organization patterns and kinetochore structures have evolved in eukaryotes ranging from yeast to humans. In addition, centromere DNA and kinetochore position can vary even within individual cells. This flexibility is manifested in several ways: centromere DNA sequences evolve rapidly, kinetochore positions shift in response to altered chromosome structure, and kinetochore complex numbers change in response to fluctuations in kinetochore protein levels. Despite their differences, all of these diverse structures promote efficient chromosome segregation. This robustness is inherent to chromosome segregation mechanisms and balances genome stability with adaptability. In this review, we explore the mechanisms and consequences of centromere and kinetochore flexibility as well as the benefits and limitations of different experimental model systems for their study.