Start with a S.R.W. Designate some points of Z^d (d>2) to be "traps" so that if a particle hits one of them it stays in it forever. The traps are placed at random independtently from each other. We are interested in identifying the maximal critical density of traps for which the random walk is still transient (that is, it eventually goes to infinity). Two cases are considered:

A) annealed, when the set of traps is updated at each unit of time;

Q) quenched, when the set of traps is fixed once and for all.

We will show that the solutions to these two cases coincide.

Next we consider an arbitrary Markov chain on any space S and show the equivalence of the annealed and quenched problems under uniform boundedness of Greens function. Moreover, assuming some geometry on the space S, a relative spherical symmetry of the density q(x) of the field of traps implies a necessary and sufficient condition for the transience. This condition consists in the finiteness of the sum, sum_{x \in S} g(x_0,x)q(x).

The talk is based on two papers: one joint with F. den Hollander and M.Menshikov, the other with R. Pemantle.