I’ll describe the various flavours of topological conformal field theory: open, closed, and open-closed. The category of open TCFTs is equivalent to that of Calabi-Yau A-infinity categories. For each open TCFT there is an associated universal closed TCFT, whose homology is the Hochschild homology of the A-infinity category. This allows us to construct the TCFT part of the higher genus B model, and to construct the TCFT part of the Gromov-Witten invariants from the Fukaya category (assuming some conjectures in symplectic topology).