The modeling and numerical simulation of complex wave propagation phenomena are discussed. The analysis and numerics of the associated partial differential equations are usually very challenging. Minor changes in the model can lead to qualitatively very different properties. The aim is therefore to find a model with mathematically good properties that is still physically justified. This requires close interaction between mathematical analysis and physical modeling. The topic is approached using examples from helioseismology, plasmonics and anisotropic wave propagation.