The shuffle-exchange permutation network (SEPn) is a fixed degree Cayley graph which has been proposed as a basis for massively parallel systems. We propose a routing algorithm with an upper bound of (5/8)n^2 + O(n), where n is the length of the permutation. (This improves on a (9/8)n^2 routing algorithm described earlier [5].) Thus, the diameter of SEPn is at most (5/8)n^2 + O(n). We also show that the diameter is at least (n^2)/2 - O(n). We demonstrate that SEPn has a Hamilton cycle, for n >= 3, left open in [5], and describe embeddings of variable degree Cayley networks, such as bubble-sort networks , star networks and pancake networks into SEPn. Our embeddings for these networks are substantial improvements of earlier results.