Given a graph where every vertex has exactly one labeled token, a swap exchanges the tokens at the two endpoints of an edge. The situation can be modelled as an exponentially large Cayley graph with a vertex for each permutation of the labels and an edge for each swap. It is easy to see that the Cayley graph is connected (every permutation of labels can be realized by a sequence of swaps). Of interest are the diameter of the Cayley graph (the worst case length of a sequence of swaps) and the complexity of computing the minimum length sequence of swaps to realize a given permutation. These token swapping problems have been studied by disparate groups of researchers in discrete mathematics, theoretical computer science, robotmotion planning, game theory, and engineering. I will survey this work and talk about hardness and approximation algorithms for token swapping on trees.