This thesis presents experiments with single 87Rb~atoms trapped in arrays of tightly confining optical tweezers. Optical tweezer arrays are a pioneering new platform for studying ultracold atomic physics and quantum computation. I begin by presenting our recent work in the preparation of large atom arrays and the quantum motional control of single atoms. Then, I present a new optical tweezer loading technique and our studies of the processes by which single atoms can be loaded near-deterministically into the microtraps. These processes depend sensitively on the long-range molecular physics of pairs of atoms, so I additionally discuss our theoretical calculations of the molecular potential landscapes relevant for such collisions. Finally, I present our all-mechanical time-of-flight-based quantum tomography of atoms in carefully prepared excited motional states of the optical tweezers
