I describe how the QCD vacuum structure, necessary to resolve the U(1)_A problem, predicts the presence of a PabbrevPparity transformation, TabbrevTtime reversal transformation, and CPabbrevCPcharge conjugation transformation followed by party transformation violating term proportional to the vacuum angle θ. To agree with experimental bounds, however, this parameter must be very small (θ < 10-9). After briefly discussing some other possible solutions to this, so-called, strong CP problem, I concentrate on the chiral solution proposed by Peccei and Quinn which has associated with it a light pseudoscalar particle, the axion. I discuss in detail the properties and dynamics of axions, focusing particularly on invisible axion models where axions are very light, very weakly coupled, and very long-lived. Astrophysical and cosmological bounds on invisible axions are also briefly touched upon.