We discuss several problems concerning domain walls in the spin-S Ising model at zero temeprature in a magnetic field, H/(2S), applied in the x direction. Some results are also given for the planar (y-z) model in a transverse field. We treat the quantum problem in one dimension by perturbation theory at small H and numerically over a large range of H. We obtain the spin-density profile by fixing the spins at opposite ends of the chain to have opposite signs of Sz. One dimensional is special in that there the quantum width of the wall is proportional to the size L of the system. We also study the quantitative features of the "particle" band which extends up to energies of order H above the ground state. Except for the planar limit, this particle band is well separated from excitations having energy J/S involving creation of more walls. At large S this particle band develops energy gaps and the lowest subband has tunnel splittings of order H21−2S. This scale of of energy gives rise to anomalous scaling with respect to (a) finite size, (b) temperature, or (c) random potentials. The intrinsic width of the domain wall and the pinning energy are also defined and calculated in certain limiting cases. The general conclusion is that quantum effects prevent the wall from being sharp and in higher dimension would prevent sudden excursions in the configuration of the wall.