I will discuss work with Cordova and Dumitrescu. We systematically analyze the possible operator content of unitary superconformal multiplets in three, and higher, spacetime dimensions. There is a surprisingly rich and exotic zoo of multiplets, and sporadic phenomena. As applications, we classify supersymmetry preserving deformations, the absolutely protected multiplets, and the conserved currents or free fields that can appear in superconformal theories. I will also discuss earlier work on the 6d a-theorem for supersymmetric theories, and some recent extensions.