  In this review article, we revisit the topic of baryogenesis, which is the
physical process that generated the observed baryon asymmetry during the first
stages of the primordial Universe. A viable theoretical explanation to
understand and investigate the mechanisms underlying baryogenesis must always
ensure that the Sakharov criteria are fulfilled. These essentially state the
following: (i) baryon number violation; (ii) the violation of both C (charge
conjugation symmetry) and CP (the composition of parity and C); (iii) and the
departure from equilibrium. Throughout the years, various mechanisms have been
proposed to address this issue, and here we review two of the most important,
namely, electroweak baryogenesis (EWB) and Grand Unification Theories (GUTs)
baryogenesis. Furthermore, we briefly explore how a change in the theory of
gravity affects the EWB and GUT baryogenesis by considering Scalar--Tensor
Theories (STT), where the inclusion of a scalar field mediates the
gravitational interaction, in addition to the metric tensor field. We consider
specific STT toy models and show that a modification of the underlying
gravitational theory implies a change in the time--temperature relation of the
evolving cosmological model, thus altering the conditions that govern the
interplay between the rates of the interactions generating baryon asymmetry,
and the expansion rate of the Universe. Therefore, the equilibrium of the
former does not exactly occur as in the general relativistic standard model,
and there are consequences for the baryogenesis mechanisms that have been
devised. This is representative of the type of modifications of the
baryogenesis processes that are to be found when considering extended theories
of gravity.
