Abstract: Ultracold polar molecules, with their rich internal structure and tunable long-range interactions, have long been proposed as a platform for quantum science. In particular, arrays of molecules individually trapped in optical tweezers promise to be a new and rich platform for quantum simulation and quantum information processing, since these arrays offer microscopic detection and control that is often desirable and sometimes necessary. In this talk, I will report on several recent advances from our group on the quantum control of laser-cooled molecules held in programmable optical tweezer arrays and discuss how they establish the building blocks for a new quantum science platform. In particular, our advances include creating defect-free molecular arrays, observing coherent interactions between molecules, and deterministically entangling molecules for the first time. I will also briefly talk about our recent work towards full quantum control of laser-cooled molecules including their motional degrees of freedom. Specifically, I will report our work on implementing Raman sideband cooling in molecules for the first time and discuss how it provides a pathway towards low-entropy molecular ensembles through laser-cooling. If time permits, I will briefly report our recent work on the first demonstration of erasure error conversion and detection in molecules, which is important in the near-term for initializing molecule arrays with high fidelity and in the longer-term for exploring measurement and feedback in quantum systems.