Olmo, Gonzalo J.Rubiera García, Diego2023-06-222023-06-222022-050218-271810.1142/S0218271822400120https://hdl.handle.net/20.500.14352/72053© 2022 World Scientific DRG is funded by the Atraccion de Talento Investigador program of the Comunidad de Madrid (Spain) No. 2018-T1/TIC-10431. This work is supported by the Spanish Grants FIS2017-84440-C2-1-P, PID2019-108485GB-I00, PID2020-116567GBC21 and PID2020-116567GB-C21 funded by MCIN/AEI/10.13039/501100011033 ("ERDF A way of making Europe" and "PGC Generacion de Conocimiento"), the project PROMETEO/2020/079 (Generalitat Valenciana), the project H2020-MSCA-RISE-2017 Grant FunFiCO-777740, the project i-COOPB20462 (CSIC), the FCT projects No. PTDC/FIS-PAR/31938/2017 and PTDC/FIS-OUT/29048/2017, and the Edital 006/2018 PRONEX (FAPESQ-PB/CNPQ, Brazil, Grant 0015/2019).In this paper, metric-afline theories in which the gravity Lagrangian is built using (projectively invariant) contractions of the Ricci tensor with itself and with the metric (Ricci-based gravity theories, or RBGs for short) are reviewed. The goal is to provide a contextualized and coherent presentation of some recent results. In particular, we focus on the correspondence that exists between the field equations of these theories and those of general relativity, and comment on how this can be used to build new solutions of physical interest. We also discuss the formalism of junction conditions in the f (R) case, and provide a brief summary on current experimental and observational bounds on model parameters.engjournal articlehttp://dx.doi.org/10.1142/S0218271822400120https://www.worldscientific.com/open access51-73Einstein equationsUniversalityLambda.Física-Modelos matemáticosFísica matemática