  Apart from the familiar structure firmly-rooted in the general relativistic
field equations where the energy--momentum tensor has a null divergence i.e.,
it conserves, there exists a considerable number of extended theories of
gravity allowing departures from the usual conservative framework. Many of
these theories became popular in the last few years, aiming to describe the
phenomenology behind dark matter and dark energy. However, within these
scenarios, it is common to see attempts to preserve the conservative property
of the energy--momentum tensor. Most of the time, it is done by means of some
additional constraint that ensures the validity of the standard conservation
law, as long as this option is available in the theory. However, if no such
extra constraint is available, the theory will inevitably carry a non-trivial
conservation law as part of its structure. In this work, we review some of such
proposals discussing the theoretical construction leading to the
non-conservation of the energy--momentum tensor.
