I review recent advances in model-building new solutions to
the strong CP problem. The new models can either enhance the axion
mass by small-size instanton effects or cancel the axion mass
mechanism by soft-breaking terms of the Peccei-Quinn symmetry. Such
models predict an axion discovery that lies outside the vanilla QCD
axion band in the $m_a$ vs.~$F_a$ plane relevant for a wide range of
haloscope, helioscope, microwave cavity, and quantum sensor
experiments.
