Ancestral processes are fundamental to modern population genetics and spatial structure has been the subject of intense interest for many years. Despite this interest, almost nothing is known about the distribution of the locations of pedigree or genetic ancestors. Using both spatially continuous and stepping-stone models, we show that the distribution of pedigree ancestors approaches a travelling wave, for which we develop two alternative approximations. The speed and width of the wave are sensitive to the local details of the model. After a short time, genetic ancestors spread far more slowly than pedigree ancestors, ultimately diffusing out with radius rather than spreading at constant speed. In contrast to the wave of pedigree ancestors, the spread of genetic ancestry is insensitive to the local details of the models.