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Abstract. The stable distribution, in its many parametrizations, is central to many stochastic processes. Many random variables that occur in the study of Lévy processes are related to it. Good progress has been made recently for simulating various quantities related to the stable law. In this note, we survey exact random variate generators for these distributions. Many distributional identities are also reviewed. Keywords and phrases. Random variate generation. Stable distribution. Lamperti’s distribution. Occupation times. Rejection method. Exact simulation. Monte Carlo methods. Expected time analysis. Probability inequalities