The Rozansky-Witten models are a family of 3-dimensional topological sigma-models that are intimately connected to the B-model, mirror symmetry, matrix factorizations, and braided monoidal deformations of the category of coherent sheaves on a complex manifold. Lots of recent work has concentrated on formulating this theory in the formalism of extended functorial field theory, i.e. presenting it as a symmetric monoidal functor of 3-categories from the extended bordism 3-category to an appropriate target 3-category C. The latter, which was studied for example by Kapustin, Rozansky, and Saulina, encodes the boundary conditions for the fields which arise from a path integral analysis of the partition function of the theory. In this talk we will sketch the ideas behind the construction of an (infinity,3)-category RW that, in many ways, approximates C in a large range of examples. We will then relate the construction to work done by Brunner, Carqueville, Fragkos, and Roggenkamp on matrix factorizations and their connection to a truncation of C. No knowledge of infinity-category theory will be required (but some might help)!