  There have been extensive studies of a random walk among a field of immobile
traps (or obstacles), where one is interested in the probability of survival as
well as the law of the random walk conditioned on its survival up to time $t$.
In contrast, very little is known when the traps are mobile. We will briefly
review the literature on the trapping problem with immobile traps, and then
review some recent results on a model with mobile traps, where the traps are
represented by a Poisson system of independent random walks on ${\mathbb Z}^d$.
Some open questions will be given at the end.
