Galaxy distances lie at the heart of the philosophical issues mentioned right after we discussed the Shapley-Curtis debate. It is only by measuring the distances to the galaxies that we can gain an appreciation of how large the Universe is. In more detail, we will want to know galaxy distances to probe the structure of the Universe: are galaxies distributed completely uniformly through space? how do galaxy motions compare with their distances? How does the number and nature of galaxies change with distance (and hence with age, since the light from more distant galaxies takes longer to reach us than light from nearer ones)?  We will show that the answers to questions like these have allowed truly fundamental advances in our understanding of the Universe, and they all depend on understanding galaxy distances.