Constitutive heterochromatin, key for the structuration of the centromeres, was long thought as a transcriptionally inert compartment, relatively invariant in composition and structure. Numerous studies have now challenged this view by showing the versatility of these epigenetically defined regions. This review highlights some important aspects of (peri)-centromeric heterochromatin structural and functional plasticity in development and differentiation. The integrity of centromeric regions is crucial for the stability of the genome and the maintenance of ploidy. I outline recent evidence suggesting that epigenetic alterations of heterochromatin can cause defects in chromosome segregation leading to aneuploidy and tumorigenesis.