  With the increasing wealth of high-quality astronomical and cosmological data
and the manifold departures from General Relativity in principle conceivable,
the development of generalized parametrization frameworks that unify
gravitational models and cover a wide range of length scales and a variety of
observational probes to enable systematic high-precision tests of gravity has
been a stimulus for intensive research. A review is presented here for some of
the formalisms devised for this purpose, covering the cosmological large- and
small-scale structures, the astronomical static weak-field regime as well as
emission and propagation effects for gravitational waves. This includes linear
and nonlinear parametrized post-Friedmannian frameworks, effective field theory
approaches, the parametrized post-Newtonian expansion, the parametrized
post-Einsteinian formalism as well as an inspiral-merger-ringdown waveform
model among others. Connections between the different formalisms are
highlighted where they have been established and a brief outlook is provided
for general steps towards a unified global framework for tests of gravity and
dark sector models.
