The raison d'être of meiosis is shuffling of genetic information via Mendelian segregation and, within individual chromosomes, by DNA crossing-over. These outcomes are enabled by a complex cellular program in which interactions between homologous chromosomes play a central role. We first provide a background regarding the basic principles of this program. We then summarize the current understanding of the DNA events of recombination and of three processes that involve whole chromosomes: homolog pairing, crossover interference, and chiasma maturation. All of these processes are implemented by direct physical interaction of recombination complexes with underlying chromosome structures. Finally, we present convergent lines of evidence that the meiotic program may have evolved by coupling of this interaction to late-stage mitotic chromosome morphogenesis.