  We survey the results required to pass between full and reduced coactions of
locally compact groups on C*-algebras, which say, roughly speaking, that one
can always do so without changing the crossed-product C*-algebra. Wherever
possible we use definitions and constructions that are well-documented and
accessible to non-experts, and otherwise we provide full details. We then give
a series of applications to illustrate the use of these techniques. We obtain
in particular a new version of Mansfield's imprimitivity theorem for full
coactions, and prove that it gives a natural isomorphism between
crossed-product functors defined on appropriate categories.
