  Modified theories of gravity that explicitly break diffeomorphism invariance
have been used for over a decade to explore open issues related to quantum
gravity, dark energy, and dark matter. At the same time, the Standard-Model
Extension (SME) has been widely used as a phenomenological framework in
investigations of spacetime symmetry breaking. Until recently, it was thought
that the SME was suitable only for theories with spontaneous spacetime symmetry
breaking due to consistency conditions stemming from the Bianchi identities.
However, it has recently been shown that, particularly with matter couplings
included, the consistency conditions can also be satisfied in theories with
explicit breaking. An overview of how this is achieved is presented, and two
examples are examined. The first is massive gravity, which includes a
nondynamical background tensor. The second is a model based on a low-energy
limit of Ho\v rava gravity, where spacetime has a physically preferred
foliation. In both cases, bounds on matter--gravity interactions that
explicitly break diffeomorphisms are obtained using the SME.
