One of the most enduring mysteries in particle physics is the nature of the non-baryonic dark matter that makes up 85% of the matter in the universe. The QCD axion, originally proposed as a solution to the strong CP problem in QCD, is one of the most strongly motivated candidates for dark matter. In this talk, I will describe the search for QCD axion dark matter with mass below ~1 micro-eV. I will discuss fundamental limits on searches for QCD axion dark matter coupled to electromagnetism, subject to the Standard Quantum Limit, and the Dark Matter Radio, an optimized electromagnetic experiment to probe the QCD axion. I will highlight the role of quantum sensors in completing this search.