The prudent self-avoiding random walk (P-SAW) is a family of self-avoiding walks in which the walk cannot take any step in the direction of a previously visited site, which is an in nite-range repellence condition. The prudent walk was originally introduced as a class of self-avoiding walks which are simple to modelize. In the last 20 years this walk has attracted the attention of the combinatorics and probability communities and, until recently, only the dimension d = 2 was completely described. In this talk we discuss the behaviour of the uniform P-SAW in high dimension. Our main result states that the P-SAW converges to Brownian motion under di usive scaling if the dimension is large enough. The same result is true for weakly prudent walk in dimension d > 5, which is greater than the critical dimension of the classical self-avoiding walk. Our approach is based on the  lace expansion. In a first part of the talk we discuss the interest to study this family of self-avoiding random walks, while in a second part we present the main tools used for the analysis of the walk.