  We review the physics potential of a next generation search for solar axions:
the International Axion Observatory (IAXO). Endowed with a sensitivity to
discover axion-like particles (ALPs) with a coupling to photons as small as
$g_{a\gamma}\sim 10^{-12}$ GeV$^{-1}$, or to electrons $g_{ae}\sim$10$^{-13}$,
IAXO has the potential to find the QCD axion in the 1 meV$\sim$1 eV mass range
where it solves the strong CP problem, can account for the cold dark matter of
the Universe and be responsible for the anomalous cooling observed in a number
of stellar systems. At the same time, IAXO will have enough sensitivity to
detect lower mass axions invoked to explain: 1) the origin of the anomalous
"transparency" of the Universe to gamma-rays, 2) the observed soft X-ray excess
from galaxy clusters or 3) some inflationary models. In addition, we review
string theory axions with parameters accessible by IAXO and discuss their
potential role in cosmology as Dark Matter and Dark Radiation as well as their
connections to the above mentioned conundrums.
