The QCD axion is not only a leading contender as a solution to the Strong CP problem, it is also a natural dark matter candidate. In particular, the post-inflationary axion has been claimed to produce a unique prediction of the axion mass if axion makes up all of dark matter. On the other hand, QCD axion models often suffers from the so-called axion quality problem, where the axion shift symmetry is unprotected from quantum gravity effects. In this talk I will discuss the tension between solutions to the quality problem and viable cosmology for post-inflationary QCD axions. I will start with a simple Z_N solution as an illustrative example of the close connection between the quality problem and the domain wall problem. I will then analyze proposals in the literature that involve more complex symmetry structure and show that they share a set of cosmological issues, including the domain wall problem and fractionally charged particles. Our study suggests that a viable post-inflationary QCD axion model is likely to have non-standard cosmological history unlike what is being assumed in recent simulations, and the “correct” axion mass to produce all of dark matter is far from certain.