Cruz Dombriz, Álvaro de laSáez Gómez, Diego2023-06-202023-06-202012-09-181099-430010.3390/e14091717https://hdl.handle.net/20.500.14352/44479© 2012 by the authors; licensee MDPI, Basel, Switzerland. AdlCD acknowledges financial support from URC and NRF (South Africa), MICINN (Spain) project numbers FIS2011-23000, FPA2011-27853-C02-01 and Consolider-Ingenio MULTIDARK CSD2009-00064.DSG acknowledges support from a postdoctoral contract from the University of the Basque Country (UPV/EHU). DSG is also supported by the research project FIS2010-15492, and also by the Basque Government through the special research action KATEA and UPV/EHU under program UFI 11/55.Along this review, we focus on the study of several properties of modified gravity theories, in particular on black-hole solutions and its comparison with those solutions in General Relativity, and on Friedmann-Lemaitre-Robertson-Walker metrics. The thermodynamical properties of fourth order gravity theories are also a subject of this investigation with special attention on local and global stability of paradigmatic f(R) models. In addition, we revise some attempts to extend the Cardy-Verlinde formula, including modified gravity, where a relation between entropy bounds is obtained. Moreover, a deep study on cosmological singularities, which appear as a real possibility for some kind of modified gravity theories, is performed, and the validity of the entropy bounds is studied.engAtribución 3.0 Españahttps://creativecommons.org/licenses/by/3.0/es/journal articlehttp://www.mdpi.com/1099-4300/14/9/1717http://www.mdpi.com/open access53Cardy-verlinde formulaEquation-of-stateDark energyf(r) gravityAccelerating universeExtended theoriesApparent horizonDesitter spacesQuantum-gravityPhantom energyFísica (Física)22 Física