  We introduce a class of composite axion models that provide a natural
solution to the strong CP problem, and possibly account for the observed dark
matter abundance. The QCD axion arises as a composite Nambu-Goldstone boson
(NGB) from the dynamics of a chiral gauge theory with a strongly-interacting
and confining SU(N) factor and a weakly-interacting U(1), with no fundamental
scalar fields. The Peccei-Quinn (PQ) symmetry is accidental and all the mass
scales are generated dynamically. We analyze specific models where the PQ
symmetry is broken only by operators of dimension 12 or higher. We also
classify several other models where the PQ symmetry can be potentially
protected up to the dimension 15 or 18 level. Our framework can be easily
extended to a scenario where the Standard Model (SM) is unified into a simple
gauge group, and we discuss the case of non-supersymmetric SU(5) unification.
The GUT models predict the existence of additional pseudo NGBs, parametrically
lighter than the GUT and PQ scales, which could have an impact on the
cosmological evolution and leave observable signatures. We also clarify the
selection rules under which higher-dimensional PQ-violating operators can
generate a potential for the axion in the IR, and provide a discussion of the
discrete symmetries in composite axion models associated to the number of
domain walls. These results can be of general interest for composite axion
models based on a QCD-like confining gauge group.
