  The tests of the constancy of the fundamental constants are tests of the
local position invariance and thus of the equivalence principle. We summarize
the various constraints that have been obtained and then describe the
connection between varying constants and extensions of general relativity. To
finish, we discuss the link with cosmology, and more particularly with the
acceleration of the Universe. We take the opportunity to summarize various
possibilities to test general relativity (but also the Copernican principle) on
cosmological scales.
