In this talk I will introduce the Strong CP problem both from a classical and a quantum field theoretical perspectives. The most convincing solution to this problem is in terms of a relaxation mechanism, realized by a light pseudo-Goldstone boson, the so-called Peccei-Quinn QCD axion. This solution, based on a non-linearly realized global U(1) symmetry, may be endangered by quantum gravity, i.e. from near Planck scale physics. The reason for this is that, suggested by string theory arguments, quantum gravity is commonly believed to break all the global symmetries. This is the so-called axion quality problem. Is there any way to give a precise and controllable estimate on how these gravitational effects may affect axion physics?
