  We discuss the advantages of using metric theories of gravity with
curvature-matter couplings in order to construct a relativistic generalisation
of the simplest version of Modified Newtonian Dynamics (MOND), where
Tully-Fisher scalings are valid for a wide variety of astrophysical objects. We
show that these proposals are valid at the weakest perturbation order for
trajectories of massive and massless particles (photons). These constructions
can be divided into local and non-local metric theories of gravity with
curvature-matter couplings. Using the simplest two local constructions in a
FLRW universe for dust, we show that there is no need for the introduction of
dark matter and dark energy components into the Friedmann equation in order to
account for type Ia supernovae observations of an accelerated universe at the
present epoch.
