In the framework of perturbed rational conformal field theories we discuss the role of topological defect lines (TDLs) in constraining bulk and boundary RG flows. For  massive RG flows with use the language of RG boundaries to describe the IR phases. Given a perturbationthat commutes or anti-commutes with some TDLs the corresponding RG boundaries  must be either invariant under the action of TDLs or be mapped between the different IR phases. For the boundary RG flows we discuss the roles of the boundary tube algebra and the symmetry-breaking TDLs. We also discuss some mathematical problems arising when one wants to systematically describe all  local operators invariant under the action of TDLs.