  We initiate the study of $T\bar T$-like irrelevant solvable deformations in
quantum field theory with boundaries and defects. For this purpose, we employ a
general formalism developed in the context of spin chains, which allows us to
derive both, the deformed bulk and boundary/defect scattering matrices of
integrable models. Using the deformed scattering matrices, we derive the flow
equation for the deformed finite volume spectrum, as well as the cylinder
partition function and the exact $g$-function.
