I will talk about work of R. Cohen and P. Norbury, who construct operations on the (co)homology of a manifold M. They consider graphs with metrics and some numbers of "incoming" and "outgoing" leaves, and map them into M according to gradient flow lines of functions on M. Such "metric graph flows" form a moduli space analogous to the moduli space of holomorphic curves in a symplectic manifold in Gromov--Witten theory. The operations can actually be constructed in equivariant (co)homology, where the automorphism group of a graph acts on products of M. They also have the structure of a TQFT, where one views the graphs as generalized (0+1)-dimensional manifolds. The cup product, intersection pairing, Steenrod squares, and Stiefel--Whitney classes all arise as examples of these operations.