Ultracold molecules have a wide range of potential applications spanning from fundamental physics to quantum simulation and computation. Motivated by potential discoveries in these areas, significant advances in controlling molecules at the single-quantum-state level have occurred over the past years. Progress in direct laser-cooling of molecules has led to the first molecular magneto-optical traps, which have allowed for optical trapping of ultracold molecules. Optical tweezer arrays have permitted both high-fidelity readout as well as quantum control of individual molecules. In this talk, we will discuss laser cooling of molecules into the ultracold regime and the creation of an optical tweezer array of CaF molecules with which we study ultracold collisions. We will also present data on rotational coherence times in optical tweezer traps, which parametrizes the potential performance of polar-molecule-based quantum simulators or computers and discuss progress we are making toward this goal with new larger arrays.

The rich structure of diatomic molecules that leads to powerful scientific avenues is qualitatively increased with polyatomic molecules. In particular, the presence of closely spaced opposite parity levels offers a new frontier in quantum science. We will present results on the laser-cooling and optical trapping of polyatomic CaOH molecules. Recent results on manipulation of states with the aforementioned parity doublet structure will also be presented.