Centromere function is essential for genome stability and chromosome inheritance. Typically, each chromosome has a single locus that consistently serves as the site of centromere formation and kinetochore assembly. Decades of research have defined the DNA sequence and protein components of functional centromeres, and the interdependencies of specific protein complexes for proper centromere assembly. Less is known about how centromeres are disassembled or functionally silenced. Centromere silencing, or inactivation, is particularly relevant in the cases of dicentric chromosomes that occur via genome rearrangements that place two centromeres on the same chromosome. Dicentrics are usually unstable unless one centromere is inactivated, thereby allowing the structurally dicentric chromosome to behave like one of the monocentric, endogenous chromosomes. The molecular basis for centromere inactivation is not well understood, although studies in model organisms and in humans suggest that both genomic and epigenetic mechanisms are involved. In this chapter, we review recent studies using synthetic chromosomes and engineered or induced dicentrics from various organisms to define the molecular processes that are involved in the complex process of centromere inactivation.