Some recent (and surprising) results on interface and contact line depinning in random media

I give a brief review of results obtained recently by several groups at Ecole Normale on the depinning transition of interfaces and contact lines, using a variety of approaches: non-local Monte Carlo algorithms, dynamical renormalization group calculations to two-loop order, and exact solution of an infinite-range model. A more direct derivation and some new results are given for the latter problem.