The functional integral methods for quantum gauge field theories allows us to pass to a symplectic formalism in order to deal with these objects in a rather nice way (the BV formalism). The extension to manifolds with boundary (the BV-BFV formalism), recently constructed by Cattaneo-Mnev-Reshetikhin, allows us to talk about cut and glue techniques in the perturbative symplectic cohomological setting for TQFTs. I will present the idea of the BV-BFV formalism and talk about several interesting connections to e.g. deformation quantization or shifted symplectic structures. Moreover, I will talk about some ideas for a higher codimension version.