We discuss the basic features of divergent versus convergent evolution and of the common scenario of parallel evolution. The example of quorum-quenching lactonases is subsequently described. Three different quorum-quenching lactonase families are known, and they belong to three different superfamilies. Their key active-site architectures have converged and are strikingly similar. Curiously, a promiscuous organophosphate hydrolase activity is observed in all three families. We describe the structural and mechanistic features that underline this converged promiscuity and how this promiscuity drove the parallel divergence of organophosphate hydrolases within these lactonase families by either natural or laboratory evolution.