The talk will be presented in two stages. In the first stage I’ll give an overview of rare-event simulation, describing techniques such as crude Monte Carlo, importance sampling, and multilevel splitting.  The next stage will describe work in progress with my Australian (well, Mexican really) supervisor Leonardo Rojas-Nandayapa, regarding maxima of dependent random variables. Our results connect properties of marginal distributions, and copula characteristics (such as upper-tail asymptotic independence) to the efficiency of a novel rare-event estimator.