  We consider the general scalar-tensor gravity without derivative couplings.
By rescaling of the metric and reparametrization of the scalar field, the
theory can be presented in different conformal frames and parametrizations. In
this work we argue, that while due to the freedom to transform the metric and
the scalar field, the scalar field itself does not carry a physical meaning (in
a generic parametrization), there are functions of the scalar field and its
derivatives which remain invariant under the transformations. We put forward a
scheme how to construct these invariants, discuss how to formulate the theory
in terms of the invariants, and show how the observables like parametrized
post-Newtonian parameters and characteristics of the cosmological solutions can
be neatly expressed in terms of the invariants. In particular, we describe the
scalar field solutions in Friedmann-Lema\^itre-Robertson-Walker cosmology in
Einstein and Jordan frames, and explain their correspondence despite the
approximate equations turning out to be linear and non-linear in different
frames.
