The nature of dark matter is one of the great mysteries of modern physics today and could be from new particles beyond the standard model. The Axion, originally conceived as a solution to the strong-CP problem in nuclear physics, is one well-motivated candidate. The Axion Dark Matter Experiment (ADMX), a DOE Gen 2 project, uses a large microwave cavity immersed in a strong static magnetic field to resonantly convert dark matter axions to detectable photons. Recently ADMX has completed its first data run with unprecedented sensitivity in the classical QCD-axion mass range of several µeV. In addition, several new detection techniques have been proposed to cover a large span of potential axion masses beyond that of the classical window. In this talk I will describe the history of axion dark matter searches, describe the recent ADMX results and give a survey of the R&D efforts currently underway to explore the entire axion dark matter mass window.