During the twentieth century, the fields of atomic and laser science learned to master the quantum states of individual atoms and ions, enabling quantum-based precision sensors of time, acceleration, and gravity, as well as new probes of the fundamental nature of our universe. A new frontier is to move beyond the current single-atom paradigm of precision measurement with atoms, and now learn to harness interactions and correlations between many atoms for realizing even more precise probes of nature. I will discuss two lines of research in this area that may allow us to overcome quantum and thermal limits on today’s best atomic precision measurements. First, I will discuss our work using collective measurements to break through the standard quantum limit, a fundamental quantum fuzziness of any measurement using independent atoms. Next, I will discuss our work to break through long-standing thermal limitations on laser linewidth by utilizing a novel gain medium: the 1 millihertz linewidth optical transition in laser-cooled strontium atoms. I will conclude by discussing our recent observation of spin exchange interactions mediated by a cavity mode.