  Modifications of general relativity provide an alternative explanation to
dark energy for the observed acceleration of the universe. We review recent
developments in modified gravity theories, focusing on higher dimensional
approaches and chameleon/f(R) theories. We classify these models in terms of
the screening mechanisms that enable such theories to approach general
relativity on small scales (and thus satisfy solar system constraints). We
describe general features of the modified Friedman equation in such theories.
  The second half of this review describes experimental tests of gravity in
light of the new theoretical approaches. We summarize the high precision tests
of gravity on laboratory and solar system scales. We describe in some detail
tests on astrophysical scales ranging from ~kpc (galaxy scales) to ~Gpc
(large-scale structure). These tests rely on the growth and inter-relationship
of perturbations in the metric potentials, density and velocity fields which
can be measured using gravitational lensing, galaxy cluster abundances, galaxy
clustering and the Integrated Sachs-Wolfe effect. A robust way to interpret
observations is by constraining effective parameters, such as the ratio of the
two metric potentials. Currently tests of gravity on astrophysical scales are
in the early stages --- we summarize these tests and discuss the interesting
prospects for new tests in the coming decade.
