  Although general relativity passes all precision tests to date, there are
several reasons to go beyond the current model of gravitation and search for
new fundamental physics. This means looking for new, so far undetected, fields.
Scalars are the easiest fields to consider and they are ubiquitous in both
extensions of the Standard Model and in alternative theories of gravity. That
is why a lot of attention has been drawn towards the investigation of
scalar-tensor theories, where gravity is described by both the metric tensor
and a scalar field.
  A particularly interesting phenomenon that has recently gained increasing
interest is spontaneous scalarization. In gravity theories that exhibit this
mechanism, astrophysical objects are identical to their general relativistic
counterpart until they reach a specific threshold, usually either in
compactness, curvature or, as recently shown, in spin. Beyond this threshold,
they acquire a nontrivial scalar configuration, which also affects their
structure.
  In this thesis, we focus on the study of this mechanism in generalized
scalar-tensor theories. We identify a minimal action that contains all of the
terms that can potentially trigger spontaneous scalarization. We first focus on
the onset of scalarization in this specific theory and determine the relevant
thresholds in terms of the contributing coupling constants and the properties
of the compact object. Finally, we study the effect of this model on the
properties of both scalarized black holes and neutron stars, such as affecting
their domain of existence or the amount of scalar charge they carry.
