Lectures on probability theory and statistics : Ecole dEté de Probabilités de Saint Flour XXXI 2001 This volume contains lectures given at the 31st Probability Summer School in Saint Flour (July 8 25 2001). Simon Tavarés contribution serves as an introduction to the coalescent and inference for ancestral processes in population genetics. Among the stochastic computation methods described are rejection methods importance sampling Markov chain Monte Carlo and approximate Bayesian methods. Ofer Zeitounis contribution on Random Walks in Random Environment presents in a systematic way the tools that have been introduced to study the model. A fairly complete description of available results in dimension 1 is given. For higher dimension the basic techniques and a discussion of some of the available results are provided. The contribution also includes an updated annotated bibliography and suggestions for further reading. TOC:Part I S. Tavaré: Ancestral Inference in Population Genetics. Part II O. Zeitouni: Random Walks in Random Environment