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Scalar fields have played an important role in the development of thefundamental theories of physics as well as in other branches of physics such asgravitation and cosmology. For a long time these escaped detection until 2012year when the Higgs boson was observed for the first time. Since thenalternatives to the general theory of relativity like the Brans-Dicke theory,scalar-tensor theories of gravity and their higher derivative generalizations-- collectively known as Horndeski theories -- have acquired renewed interest.In the present review we discuss on several selected topics regarding thesetheories, mainly from the theoretical perspective but with due mention of theobservational aspect. Among the topics covered in this review we pay specialattention to the following: 1) the asymptotic dynamics of cosmological modelsbased in the Brans-Dicke, scalar-tensor and Horndeski theories, 2) inflationarymodels, extended quintessence and the Galileons, with emphasis in causality andstability issues, 3) the chameleon and Vainshtein screening mechanisms that mayallow the elusive scalar field to evade the tight observational constraintsimplied by the solar system experiments, 4) the conformal frames conundrum witha brief discussion on the disformal transformations and 5) the role of Weylsymmetry and scale invariance in the gravitation theories. The review is aimedat specialists as well as at non-specialists in the subject, includingpostgraduate students.

Selected topics in scalar-tensor theories and beyond