  . In this paper we give a survey of some recent results for random walk in
random scenery (RWRS). On $\mathbb {Z}^d$, $d\geq 1$, we are given a random
walk with i.i.d. increments and a random scenery with i.i.d. components. The
walk and the scenery are assumed to be independent. RWRS is the random process
where time is indexed by $\mathbb {Z}$, and at each unit of time both the step
taken by the walk and the scenery value at the site that is visited are
registered. We collect various results that classify the ergodic behavior of
RWRS in terms of the characteristics of the underlying random walk (and discuss
extensions to stationary walk increments and stationary scenery components as
well). We describe a number of results for scenery reconstruction and close by
listing some open questions.
