  We review current cosmological constraints on the axion. We describe the
basic mechanisms by which axions are created in the early universe, focussing
on the standard thermal scenario where the dominant process is through axion
radiation by a string network. A dark matter axion in this case would have a
mass $\ma \sim 100 \microeV$, with specified large uncertainties. This
cosmological lower bound leaves a viable window for the axion below the
astrophysical upper limit, $\ma \lapp 1-10 \meV$. We also discuss alternative
axion cosmologies which allow a much wider, but indefinite, mass range.
