  We are interested in the behaviour of the range of the Campanino and
P\'etritis random walk, namely a simple random walk on the lattice $\mathbb
Z^2$ with random orientations of the horizontal layers. We also study the range
of random walks in random scenery, from which the asymptotic behaviour of the
range of the first coordinate of the Campanino and P\'etritis random walk can
be deduced.
