In this lecture we are concerned with the study of the asymptotic behaviour of a multi-dimensional Fisher-KPP equation posed in an asymptotically homogeneous medium and supplemented together with a compactly supported initial datum. We derive precise estimates for the location of the front before proving the convergence of the solutions towards travelling front. In particular we show that the location of the front drastically depends on the rate at which the medium becomes homogeneous at innity. Fast rate of convergence only changes the location by some constant while lower rate of convergence induces further logarithmic delay.