The seismic records from significant earthquakes are profoundly affected by 3-D variations in crustal structure both in the source zone itself and in propagation to some distance. Even in structurally complex zones such as Japan and Mexico relatively coherent arrivals are found associated with different classes of propagation paths. The presence of strong lateral variations can disrupt the arrivals, and such effects can be modelled using a combination of simple ray concepts and detailed numerical modelling using e.g. the pseudospectral method. Where detailed structural control is available, 3-D computations can capture the character of the observations.