Importance sampling is one of the key classical methods for estimating integrals. I will talk through some of the things we need to think about when building robust, implementations of importance sampling that will fail noisily. In particular, I will focus on a variant of importance sampling, known as Pareto-Smoothed Importance Sampling, which trades off some small finite-sample bias with good stability properties and a built-in heuristic. I will also talk through some of the theory and open questions. And suggest that some amount of importance sampling may well be useful even when computing integrals isn't our main aim.