We argue that parameterized complexity is a useful tool with which to study global constraints. In particular, we show that many global constraints which are intractable to propagate completely have natural parameters which make them fixed- parameter tractable and which are easy to compute. This tractability tends either to be the result of a simple dynamic program or of a decomposition which has a strong backdoor of bounded size. This strong backdoor is often a cycle cutset. We also show that parameterized complexity can be used to study other aspects of constraint programming like symme- try breaking. For instance, we prove that value symmetry is fixed-parameter tractable to break in the number of symme- tries. Finally, we argue that parameterized complexity can be used to derive results about the approximability of constraint propagation.