  We briefly review the principles, mathematical bases, numerical shortcuts and
applications of fast random walk (FRW) algorithms. This Monte Carlo technique
allows one to simulate individual trajectories of diffusing particles in order
to study various probabilistic characteristics (harmonic measure, first
passage/exit time distribution, reaction rates, search times and strategies,
etc.) and to solve the related partial differential equations. The adaptive
character and flexibility of FRWs make them particularly efficient for
simulating diffusive processes in porous, multiscale, heterogeneous, disordered
or irregularly-shaped media.
