We present results on embeddings of groups of polynomial growth into Euclidean and L^p spaces. More precisely, if the group is not virtually abelian, the ball of radius n incurs bilipschitz distortion sqrt(log n) into L^2 spaces and into a Euclidean space whose dimension depends only on the group. We present a coarse differentiation technique in a more abstract setting and discuss its implications on embeddability. Part of this talk is based on a result joint with Hyun Chul Jang.
