Abstract: Control over interactions and measurements in quantum systems is crucial for applications such as quantum simulation and computation. In this talk, I will highlight our recent progress in realizing nondestructive readout and long-range interactions in atomic tweezer arrays using a strongly coupled optical cavity. Through selectively coupling a single atom with the cavity mode, we achieve a rapid mid-circuit measurement without perturbing the quantum coherence of the other atoms. Conversely, the collective emission from multiple atoms into the cavity can be coherently enhanced or suppressed. By controlling the atom-cavity interaction at the single-atom level, we observe both super- and subradiant cavity emissions from the constructed atomic ensembles. I will then discuss how we engineer long-range mechanical interactions via photon exchange and present our recent observation of a self-organization phase transition in a mesoscopic system. Finally, I will discuss how the cavity can be used to monitor and manipulate strongly interacting quantum gases, opening new avenues for experimental research in quantum many-body physics.