The axion is a hypothetical particle which would explain why QCD is approximately T-conserving, and is also an excellent Cold Dark Matter candidate. It should be possible to make a clean theoretical prediction relating the dark matter density in axions and the axion mass (under reasonable assumptions about inflation). But the axion's early-Universe dynamics, which establish its density as dark matter, are unexpectedly rich in a way which is only starting to yield to quantitative numerical study.