Reshetikhin and Turaev, motivated by Witten's work on Chern-Simons theory, constructed 1-2-3 field theories from modular tensor categories. In ongoing joint work with Constantin Teleman we aim to construct an invertible 4-dimensional field theory from a modular tensor category, and then use the cobordism hypothesis to construct a companion 0-1-2-3 theory which extends the Reshetikhin-Turaev theory as an anomalous field theory. I will explain these ideas in a more general context and indicate the techniques we are using.