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A hybrid combination of theories, containing elements from both of these formalisms, turns out to be very successful in accounting for the observed phenomenology and it is able to avoid some drawbacks of the original approaches. Here, we explore the formulation of this hybrid metric-Palatini approach and its main achievements in passing the local tests and several applications to astrophysical and cosmological scenarios. More specifically, we present the weak-field limit, analyze the well-posedness of the Cauchy problem for the hybrid model and explore the viability of generalized hybrid metric-Palatini gravitational theories. <\/jats:p>","DOI":"10.1142\/s021988782330009x","type":"journal-article","created":{"date-parts":[[2023,7,21]],"date-time":"2023-07-21T07:28:07Z","timestamp":1689924487000},"source":"Crossref","is-referenced-by-count":2,"title":["Hybrid metric-Palatini gravity: General formalism and applications"],"prefix":"10.1142","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9388-8373","authenticated-orcid":false,"given":"Francisco S. 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