Abstract: Trapping single atoms with optical tweezers, cooling the atoms to the ground state to form ultracold atoms, coherently controlling them to form single ultracold molecules, then rearranging them into a rich and diverse array of ultracold single atoms and molecules, all of these steps create a precise and coherently controllable multi-particle quantum system, and provide a rare quantum platform for a variety of frontier scientific research and technology development. This article reviews the latest progress in the study of ultracold single atom and molecule arrays. Recent results on high fidelity control of quantum states of single atoms, heteronuclear quantum entanglement, coherent control of atom-molecule states, coherent formation of a single molecule, and deterministic preparation of heteronuclear atom arrays are outlined. The future prospects in many-body physics, ultracold chemistry, precision measurement, quantum simulation and quantum computation are presented.