Although we know that many supernovae are aspherical, the exact nature of their geometry is undetermined. Because all the supernovae we observe are too distant to be resolved, the ejecta structure can't be directly imaged, and asymmetry must be inferred from signatures in the spectral features and polarization of the supernova light. The empirical interpretation of this data, however, is rather limited--to learn more about the detailed supernova geometry, theoretical modeling must been undertaken. One expects the geometry to be closely tied to the explosion mechanism and the progenitor star system, both of which are still under debate. Studying the 3-dimensional structure of supernovae should therefore provide new break throughs in our understanding. The goal of this thesis is to advance new techniques for calculating radiative transfer in 3-dimensional expanding atmospheres, and use them to study the flux and polarization signatures of aspherical supernovae. We develop a 3-D Monte Carlo transfer code and use it to directly fit recent spectropolarimetric observations, as well as calculate the observable properties of detailed multi-dimensional hydrodynamical explosion simulations. While previous theoretical efforts have been restricted to ellipsoidal models, we study several more complicated configurations that are tied to specific physical scenarios. We explore clumpy …