A long-standing theme of atomic physics is a continual striving to gain ever greater control over single quantum objects, starting with their internal degrees of freedom and now extending to their external degrees of freedom. Having learned to exert nearly complete control over single atoms, what are the new frontiers? One direction is to now exert similar levels of control over the interactions and correlations between atoms, with examples including quantum computing with trapped ions, quantum many-body simulations in degenerate atomic gases, and the deterministic assembly of molecules. Our lab has been asking the question: is it also possible to exploit atom-atom correlations and entanglement to advance the field of precision measurement beyond the single-atom paradigm that dominates the field? Using laser-cooled and trapped rubidium and strontium atoms inside of high finesse optical cavities, we have explored this question along two fronts by surpassing the standard quantum limit on quantum phase estimation by a factor of 60 and overcoming thermal limits on laser frequency stability. If time permits, I will also discuss the emergence of spin-exchange interactions between atoms mediated by the optical cavity. Possible future impacts include robust millihertz linewidth optical lasers, advanced optical lattice clocks, and searches for new physics.