At a discontinuity in material properties - an interface - multiple rays or waves are generated. For an individual ray, the ray properties - direction, amplitudes and polarizations - are discontinuous. This chapter describes the discontinuities in these results, i.e. Snell's law (direction), the dynamic ray discontinuity (geometrical spreading), and reflection/transmission coefficients (amplitude and polarizations). The reflection/transmission coefficients are developed in a general manner for acoustic, elastic and fluid-solid interfaces which, with the correct normalizations, emphasizes relationships between different coefficients. At an interface, several rays combine and the response is not given by a simple ray polarization. The necessary receiver conversion coefficients, particularly at a free surface, are derived. A procedure for linearly perturbing the coefficients is developed. These perturbation or differential coefficients are particularly useful for obtaining approximate coefficients from a weak-contrast interface. In the final section, the concept of an individual ray is generalized to a ray table characterized by a ray signature. This is used to generalize the ray Green dyadic to include interfaces.