In this talk I will present a multilevel subset estimator for rare event probabilities. The proposed estimator uses different model resolutions and varying numbers of samples on the hierarchy of failure sets. We construct the failure sets such that a high number of samples are used when the model evaluations are cheap, while only using a small number of expensive samples, in order to reduce the computational cost. A key idea in our new estimator is the use of a posteriori error estimation to guarantee the critical subset property that may be violated when changing model resolution from one failure set to the next. The computational gains are demonstrated on a model elliptic PDE with random coefficients. This is joint work with Daniel Elfverson.