Nanometer structures in semiconductor heterojunction systems have been studied for several years and have conclusively shown evidence for quantum interference phenomena and granular effects due to the finite number of electrons and impurities. Various proposals have been made for novel devices based on such effects, which would serve as the basis for terabit memories and ultra-dense processing elements. A discussion is given of the application of a generalized mode-matching scheme as a computational tool for investigating arbitrary quantum waveguide structures and discontinuities. Results are presented for the nonlinear conductance properties of multiple bend structures, lateral resonant tunnel structures, and nonequilibrium transport through quantum dot structures. Comparison is made to various experimental realizations of these structures where complications due to undesired inhomogeneities, such as boundary roughness and impurities, play a significant role.