  Random Walks in Dirichlet Environment (RWDE) correspond to Random Walks in
Random Environment (RWRE) on $\Bbb{Z}^d$ 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 $(\alpha_i)_{i=1, \ldots, 2d}$,
one for each direction of $\Bbb{Z}^d$. 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 give a state of the art on this model and several sketches of
proofs presenting the core of the arguments. We also present new computation of
the large deviation rate function for one dimensional RWDE.
