  We discuss the appearance at the QCD phase transition, and the subsequent
decay, of axion walls bounded by strings in N=1 axion models. We argue on
intuitive grounds that the main decay mechanism is into barely relativistic
axions. We present numerical simulations of the decay process. In these
simulations, the decay happens immediately, in a time scale of order the light
travel time, and the average energy of the radiated axions is $<\omega_a >
\simeq 7 m_a$ for $v_a/m_a \simeq 500$. $<\omega_a>$ is found to increase
approximately linearly with $\ln(v_a/m_a)$. Extrapolation of this behaviour
yields $<\omega_a> \sim 60 m_a$ in axion models of interest. We find that the
contribution to the cosmological energy density of axions from wall decay is of
the same order of magnitude as that from vacuum realignment, with however large
uncertainties. The velocity dispersion of axions from wall decay is found to be
larger, by a factor $10^3$ or so, than that of axions from vacuum realignment
and string decay. We discuss the implications of this for the formation and
evolution of axion miniclusters and for the direct detection of axion dark
matter on Earth. Finally we discuss the cosmology of axion models with $N>1$ in
which the domain wall problem is solved by introducing a small U$_{PQ}$(1)
breaking interaction. We find that in this case the walls decay into
gravitational waves.
