  The increased collecting area of the ELTs will bring fainter high-z targets
within the reach of high-resolution ultra-stable spectrographs, thus enabling a
new generation of precision consistency tests, including tests of the stability
of nature's fundamental couplings. For example, the stability of the
fine-structure constant can be tested by looking at metal absorption lines
produced by the intervening clouds along the line of sight of distant quasars.
  In this contribution, we discuss the performance that can be expected from
the ELTs in testing the stability of the fine-structure constant, based on the
early ESPRESSO observations, and some comparative forecasts of the impact of
these measurements for representative models of fundamental physics and
cosmology.
