Meiosis is a conserved eukaryotic cell division that increases genetic diversity in sexual populations. During meiosis homologous chromosomes pair and undergo recombination that can result in reciprocal genetic exchange, termed crossover. The frequency of crossover is highly variable along chromosomes, with hot spots and cold spots. For example, the centromeres that contain the kinetochore, which attach chromosomes to the microtubular spindle, are crossover cold spots. Plant centromeres typically consist of large tandemly repeated arrays of satellite sequences and retrotransposons, a subset of which assemble CENH3-variant nucleosomes, which bind to kinetochore proteins. Although crossovers are suppressed in centromeres, there is abundant evidence for gene conversion and homologous recombination between repeats, which plays a role in satellite array change. We review the evidence for recombination within plant centromeres and the implications for satellite sequence evolution. We speculate on the genetic and epigenetic features of centromeres that may influence meiotic recombination in these regions. We also highlight unresolved questions relating to centromere function and sequence change and how the advent of new technologies promises to provide insights.