We pretty much do. That is, matter within the universe move in all directions, towards us, away from us, at various angles with respect to us. This is superimposed upon the general expansion of space, which tends to move every point away from every other point, but only manifests itself outside of the local galactic supergoup, at about 200 million lys. Closer that that we don't see expansion because gravity is stronger on that scale. There is no center of the universe. On the large scale, every point appears to be the center, because everything is moving away from it.