The linear operator that relates the normal gradient of a wave field to its values on an irregular surface is the basis for a new formulation of the rough‐surface scattering problem. This formulation has led to a class of approximations that surpass traditional methods in accuracy and efficiency. The connection between this approach and the standard formulation by means of a boundary integral equation is the subject of this paper. While equivalent in all respects, the admittance operator formulation provides helpful new perspectives on the physics of surface scattering and lends itself naturally to more elaborate problems. For example at a rough boundary between dissimilar media, the operators compose themselves into generalized reflection and transmission operators; while at a random surface the operator terms lead to analytic forms for the scattered field moments.