What are the ultimate limits for how small we can make computing devices? What fundamental constraints does physics impose, either in size, speed, or heat dissipation? For the past several years my group has been investigating these questions in the context of a new transistor-less paradigm known as Quantum-dot Cellular Automata (QCA). QCA was invented and developed here and is now the subject of research world-wide. QCA enables binary computing which can be scaled down to the single-molecule size scale. QCA has been explored in metal-dot, GaAs, Si, nanomagnetic, and molecular systems. This is a theoretical group, but we work closely with solid-state experimentalist, chemists, and computer scientists, examining the particular issues of each implementation, and the energetic, architectural, and thermodynamic considerations that apply to all implementations. Recent work has focused particularly on understanding single-molecule QCA behavior, and on the connection to broader questions in information theory and the thermodynamics of computation.