The nature of cold dark matter (CDM) is one of the largest outstanding questions in particle physics, and the axion, a hypothetical boson originally postulated to explain the startling absence of CP violation in the strong interactions, is widely considered one of the best motivated candidates. The axion's extremely low mass (<< 1 meV) and weak coupling to standard model fields motivates detectors which are very unusual from the standpoint of experimental particle physics. One such detector is the "axion haloscope," which consists of an extremely quiet microwave receiver coupled to a high-Q cavity immersed in a strong magnetic field. In this talk I will briefly motivate axions and dark matter, introduce the basic principles of haloscope detection, and discuss my thesis research building and operating the Haloscope At Yale Sensitive To Axion CDM (HAYSTAC). Wih the first results from HAYSTAC we have demonstrated cosmologically relevant sensitivity an order of magnitude higher in mass than any existing limits on axions, and achieved noise performance approaching the standard quantum limit for the first time in an axion search.