TY - JOUR AB - 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. AU - Belenchia, Alessio AU - Letizia, Marco AU - Liberati, Stefano AU - Di Casola, Eolo DA - 2018/02/09/ DO - 10.1088/1361-6633/aaa4ab IS - 3 JF - Reports on Progress in Physics PY - 2018 SE - 2018/02/09/ SP - 036001 TI - Higher-order theories of gravity: diagnosis, extraction and reformulation via non-metric extra degrees of freedom-a review UR - https://iopscience.iop.org/article/10.1088/1361-6633/aaa4ab VL - 81 ER -