Null field integral techniques are a powerful means for solving scattering problems when the scatterer is impenetrable or penetrable, but homogeneous. The immediate and obvious advantage it has over volume discretization techniques, such as finite element or finite difference, is that only the surface, not the volume, is discretized, thus, the number of unknowns is decreased from n 3 to n 2. The number of unknowns can be further reduced to increase the accuracy obtainable in the problem by representing an unknown interfacial function (such as the axially directed electric field on a dielectric wedge) in terms of interpolative global basis functions, where the function to be approximated is defined by an integral equation. Although some art is required in choosing appropriate basis functions, the average researcher should not be deterred from deriving an appropriate set for his own particular applications. We focus on two null field techniques, which are distinguished by whether or not one chooses to represent the Green's function as a “partial wave expansion”. In the first half of this paper, we exploit a null field technique which does not involve a Green's function expansion, but retains its normal two- or three-dimensional representation. We choose electromagnetic scattering from a penetrable wedge as a representative example of a problem ideally suited to this first null field technique; the penetrable wedge is a classical scattering problem and have no closed-form analytical solution. The two principle difficulties in the wedge problem—singularities near the wedge apex and the unboundedness of the wedge itself—make it difficult to trace refracted and reflected waves internally. In the second half of this paper, we extend a null field technique to include those cases where both the unknown scattered field in question and the Green's function can be expanded in orthonormal partial wave function sets. This extension allows the integrals representing those fields to be written immediately as sums of the partial wave functions. Determination of the fields then reduces to matrix inversion, this matrix is commonly referred to as the transition matrix, or T-matrix. With this second null field technique, the method of constructing this matrix and its inversion often presents serious challenges to the numerical analyst. We apply the T-matrix technique to acoustical scattering from a soft spheroid, and scattering from a thin aluminum elastic shell. Numerical results for both null field methods are presented and discussed in the context of previous results.