"There are viable theories and there are natural and elegant theories. However, all viable, natural and elegant theories contain dark-matter axions" - Ann Nelson. Physics has two perplexing mysteries: What suppresses the expected large amount of CP violation in the strong interactions (the "Strong CP Problem") and the nature of dark matter. The axion is a hypothetical elementary particle originally postulated to solve the strong CP problem. The axion is also an extremely attractive dark matter candidate. The axion is the puzzle piece allowing these two mysteries to fit naturally into our understanding of the universe.
The axion was originally postuated to exist as part of the solution to the "Strong CP Problem". This problem arose from the observation that the strong force holding nuclei together and the weak force making nuclei decay differ in the amount of CP violation in their interactions. Weak-interaction was expected to feed into the strong interactions (QCD), yielding appreciable QCD CP violation, but no such violation has been observed to very high accuracy. One solution to this Strong CP Problem ends up introducing a new particle called the axion. If the axion is very light, it interacts so weakly that it would be nearly impossible to detect but would be an ideal dark matter candidate. The ADMX experiment aims to detect this extraordinarily weakly-coupled particle.
Although dark matter can't be seen directly, its gravitational interactions with familiar matter leave unmistakable evidence for its existence. The universe we see today simply wouldn't look the way it does without dark matter. Approximately five times more abundant than ordinary matter, the nature of dark-matter remains one of the biggest mysteries in physics today.
In addition to solving the strong CP problem, the axion could provide an answer to the question "what is dark matter made of?" The axion is a neutral particle that is extraordinarily weakly interacting and could be produced in the right amount to constitute dark matter. If the dark-matter accounting for the bulk of all matter in our universe is axions, there is only one experiment in the world that is sensitive enough to discover it; that experiment is ADMX.