  We study four-dimensional superconformal field theories coupled to
three-dimensional superconformal boundary or defect degrees of freedom.
Starting with bulk N=2, d=4 theories, we construct abelian models preserving
N=2, d=3 supersymmetry and the conformal symmetries under which the
boundary/defect is invariant. We write the action, including the bulk terms, in
N=2, d=3 superspace. Moreover we derive Callan-Symanzik equations for these
models using their superconformal transformation properties and show that the
beta functions vanish to all orders in perturbation theory, such that the
models remain superconformal upon quantization. Furthermore we study a model
with N=4 SU(N) Yang-Mills theory in the bulk coupled to a N=4, d=3
hypermultiplet on a defect. This model was constructed by DeWolfe, Freedman and
Ooguri, and conjectured to be conformal based on its relation to an AdS
configuration studied by Karch and Randall. We write this model in N=2, d=3
superspace, which has the distinct advantage that non-renormalization theorems
become transparent. Using N=4, d=3 supersymmetry, we argue that the model is
conformal.
