Let H-0 = (i del - A)(2) be the Schrodinger operator with constant magnetic field in R-d, d = 2,3 and K subset of R-d be a compact domain with smooth boundary. We consider the Dirichlet (resp. Neumann, resp. Robin) realization of (i del - A)(2) on Omega := R-d \ K. First, in the case d = 2, we recall the known results concerning eigenvalue clusters for these exterior problems. Then, in dimension 3, after a review on the previous results for potential perturbations, we study the resonances for the obstacle problems. We establish the existence of resonance free sectors near the Landau level and study a resonance counting function. Consequently we obtain the accumulation of resonances at the Landau levels and in some cases the discretness of the set of the embedded eigenvalues.