Abstract: Ultracold polar molecules are promising candidate qubits for quantum computing and quantum simulations. Their long-lived molecular rotational states form robust qubits, and the long-range dipolar interaction between molecules provides quantum entanglement. We demonstrate dipolar spin-exchange interactions between single CaF molecules trapped in an optical tweezer array. We realized the spin-1/2 quantum XY model by encoding an effective spin-1/2 system into the rotational states of the molecules and used it to generate a Bell state through an iSWAP operation. Conditioned on the verified existence of molecules in both tweezers at the end of the measurement, we obtained a Bell state fidelity of 0.89(6). Using interleaved tweezer arrays, we demonstrate single-site molecular addressability. Recently, we demonstrated Raman sideband cooling of CaF molecules in optical tweezers to near their motional ground state, with a 3-D motional ground state probability of 54%. This paves the way to increase molecular coherence times in optical tweezers for quantum applications.