The dark matter puzzle is one of the most important open problems in modern fundamental physics. I will describe some of the approaches that are used to search for non-gravitational interactions of ultralight dark matter, and the fundamental limitations on their sensitivity. The axion is a compelling dark matter candidate, since it resolves the strong-CP problem of quantum chromodynamics. I will focus on precision laboratory-scale experiments that search for axion-like dark matter, aiming to achieve, or circumvent, the quantum limits on their sensitivity. Specifically, the Cosmic Axion Spin Precession Experiment (CASPEr-e) uses nuclear magnetic resonance to search for the defining gluon coupling of the QCD axion. The prototype CASPEr-e experiment has achieved design sensitivity in the nano-electronvolt mass range. We are now developing the next-generation search, with the goal of achieving the sensitivity at the QCD axion level.