Axions are ubiquitous in string theory compactifications. They are

pseudo goldstone bosons and can be extremely light, contributing to

the dark sector energy density in the present-day universe. The

mass defines a characteristic length scale. For 1e-33 eV<m< 1e-20

eV this length scale is cosmological and axions display novel

effects in observables. The magnitude of these effects is set by

the axion relic density. The axion relic density and initial

perturbations are established in the early universe before, during,

or after inflation (or indeed independently from it). Constraints

on these phenomena can probe physics at or beyond the GUT scale. I

will present multiple probes as constraints of axions: the Planck

temperature power spectrum, the WiggleZ galaxy redshift survey,

Hubble ultra deep field, the epoch of reionisation as measured by

cmb polarisation, cmb b-modes and primordial gravitational waves,

and the density profiles of dwarf spheroidal galaxies. Together

these probe the entire 13 orders of magnitude in axion mass where

axions are distinct from CDM in cosmology, and make non-trivial

statements about inflation and axions in the string landscape. The

observations hint that axions in the range 1e-22 eV<m<1e-20 eV may

play an interesting role in structure formation, and evidence for

this could be found in the future surveys AdvACT (2015), JWST, and

Euclid (>2020). If inflationary B-modes are observed, a wide range

of axion models including the anthropic window QCD axion are

excluded unless the theory of inflation is modified. I will also

comment briefly on direct detection of QCD axions.