  Modifications of Einstein's theory of gravitation have been extensively
considered in the past years, in connection to both cosmology and quantum
gravity. Higher-curvature and higher-derivative gravity theories constitute the
main examples of such modifications. These theories exhibit, in general, more
degrees of freedom than those found in standard General Relativity; counting,
identifying, and retrieving the description/representation of such dynamical
variables is currently an open problem, and a decidedly nontrivial one. In this
work we review, via both formal arguments and custom-made examples, the most
relevant methods to unveil the gravitational degrees of freedom of a given
model, discussing the merits, subtleties and pitfalls of the various
approaches.
