A rich class of d-dimensional field theories arises when placing M-theory on codimension (11-d) singularities. I will discuss how (d+1)-dimensional topological field theories (TQFTs) encode the (higher) symmetries and anomalies of these d-dimensional theories, and how these TQFTs can be extracted from the geometry of the singular space. I will illustrate the discussion by analysing some simple examples explicitly.