The atom tweezer array is changing how many of us think about and perform AMO physics.  My laboratory at Berkeley has adopted this technique by placing atom arrays within a high-cooperativity optical cavity.  Our work follows two threads.  In one, we use the capabilities of atom arrays to explore one of the main topics studied in cavity QED, which is the behavior of optically driven atom-cavity systems as an open many-body quantum system.  I will describe experiments on self-organization in both the mechanical and spin degrees of freedom of a cavity-coupled tweezer array, and indicate new directions afforded by the programmability of our setup.  A second thread investigates how cavity QED can be used to advance the many uses of atom tweezer arrays.  Here, I will describe our recent success in performing fast mid-circuit measurement and feed-forward control by leveraging cavity-enhanced detection, and progress toward operating a Rydberg array quantum microprocessor with a high-cooperativity optical cavity.