We examine the geometrical and topological properties of surfaces surrounding clusters in the 3d Ising model. For geometrical clusters at the percolation temperature and Fortuin-Kasteleyn clusters at T c , the number of surfaces of genus g and area A behaves asA x ( g ) e - μ ( g ) A , with x approximately linear in g and μ constant. These scaling laws are the same as those we obtain for simulations of 3d bond percolation. We observe that cross sections of spin domain boundaries atT c decompose into a distribution N(l) of loops of length l that scales asl - τ with τ 2.2. We also present some new numerical results for 2d self-avoiding loops that we compare with analytic predictions. We address the prospects for a string-theoretic description of cluster boundaries.