In this article we review the state of play in the use of stochastic models for the measurement and management of longevity risk. A focus of the discussion concerns how robust these models are relative to a variety of inputs: something that is particularly important in formulating a risk management strategy. On the modeling front much still needs to be done on robust multipopulation mortality models, and on the risk management front we need to develop a better understanding of what the objectives are of pension plans that need to be optimized. We propose a variety of ways forward on both counts.