Random Walks in Dirichlet Environment (RWDE) correspond to Random Walks in Random Environment (RWRE) on Zd where the transition probabilities are i.i.d. at each site with a Dirichlet distribution. Hence, the model is parametrized by a family of positive weights (αi)i=1,...,2d, one for each oriented direction of Zd. In this case, the annealed law is that of a reinforced random walk, with linear reinforcement on directed edges. RWDE have a remarkable property of statistical invariance by time reversal from which can be inferred several properties that are still inaccessible for general environments, such as the equivalence of static and dynamic points of view and a description of the directionally transient and ballistic regimes. In this paper we review the recent developments on this model and give several sketches of proofs presenting the core of the arguments. We also present new computations of the large deviation rate function for one dimensional RWDE.