The QCD axion, originally proposed as a solution to the strong CP problem, is also a well motivated dark-matter candidate. Recently, a number of experimental proposals have emerged to search for QCD axion dark matter over the entire allowed mass range (~1 peV-1 eV). I discuss fundamental limits on searches for QCD axion dark matter, subject to the Standard Quantum Limit on phase-insensitive amplification. Single-pole resonators can approach the fundamental limit of sensitivity for probes of axion dark matter, and the optimization of measurement backaction and sensitivity outside of the resonator bandwidth can increase scan rates by up to five orders of magnitude at low frequency. I also discuss the application of quantum sensing techniques to evade the Standard Quantum Limit on amplification and enable a complete probe of QCD axion dark matter below 1 ueV. I describe the first results from the Dark Matter Radio (DM Radio), a tunable, lumped-LC resonant search for axion and hidden photon dark matter between ~1 peV and ~1 ueV. The prototype detector, the DM Radio Pathfinder, uses a 4K liquid-helium-cooled detector to search for hidden photons in the 500 peV-50 neV mass range.