The QCD axion provides an elegant solution to the Strong CP problem and could be some or all of the dark matter of our universe. This prospect, however, is challenged when taking into account symmetry breaking effects from quantum gravity, leading to what is known as the axion quality problem. In this talk, I introduce 'big axions': a general class of axion models that address the quality problem using collective symmetry breaking in an extended theory space. I show that these models admit rich structure that effectively interpolates between ordinary 4D Peccei-Quinn axions and axions descending from extra-dimensional gauge fields. I then study an explicit example of a big axion and show how it can be the QCD axion of our universe, highlighting in particular its rich post-inflationary cosmological dynamics.