Abstract:  Conformal Field Theories (CFTs) have a highly constrained structure that make them much more tractable, especially at strong coupling, than generic QFTs.  An appealing picture for more general QFTs is as points along the RG flow from a UV CFT.  We discuss conformal truncation as a method for nonperturbatively following such RG flows.  We describe some examples of past and potential applications, and in particular some of the advantages of the method for studying gauge theories, as well as remaining challenges.