Since the pioneering model for homologous recombination proposed by Robin Holliday in 1964, there has been great progress in understanding how recombination occurs at a molecular level. In the budding yeast Saccharomyces cerevisiae, one can follow recombination by physically monitoring DNA after the synchronous induction of a double–strand break (DSB) in both wild–type and mutant cells. A particularly well–studied system has been the switching of yeast mating–type (MAT) genes, where a DSB can be induced synchronously by expression of the site–specific HO endonuclease. Similar studies can be performed in meiotic cells, where DSBs are created by the Spo11 nuclease. There appear to be at least two competing mechanisms of homologous recombination: a synthesis–dependent strand annealing pathway leading to noncrossovers and a two–end strand invasion mechanism leading to formation and resolution of Holliday junctions (HJs), leading to crossovers. The establishment of a modified replication fork during DSB repair links gene conversion to another important repair process, break–induced replication. Despite recent revelations, almost 40 years after Holliday's model was published, the essential ideas he proposed of strand invasion and heteroduplex DNA formation, the formation and resolution of HJs, and mismatch repair, remain the basis of our thinking.