Ultracold molecules confined in optical lattices or tweezer traps offer promising platforms for quantum simulation and quantum computation. These molecules possess a large number of stable states with long coherence times, enabling precise control over their internal and external states. They can be prepared in desired states with high fidelity and are capable of generating long-range dipole-dipole interactions, which are essential for entanglement and many-body quantum states. The review discusses recent advances and challenges in this field, highlighting the potential of ultracold molecules for quantum simulation and computation. Molecules can be used to encode spin or qubit states in their rotational levels, allowing for the simulation of spin models and quantum information processing. Theoretical models, such as the dipolar XXZ model, demonstrate the potential for studying various quantum phases and interactions. Experimental progress includes the observation of spin-exchange interactions and the implementation of quantum gates using dipolar spin-exchange interactions. These experiments have shown that even low lattice fillings can exhibit dipolar interactions, paving the way for the study of many-body dynamics in disordered systems. Challenges include suppressing losses in molecular systems and achieving high fillings in optical lattices. Techniques such as shielding and dynamic decoupling have been employed to mitigate these issues. Additionally, the development of quantum gas microscopes has enabled site-resolved measurements of spin dynamics, providing insights into the anisotropy of dipolar interactions. For quantum computation, molecules provide stable qubits with long coherence times and the ability to generate entanglement through dipolar interactions. Recent experiments have demonstrated deterministic entanglement of molecule pairs using spin-exchange interactions, achieving high fidelity. Scaling up these systems to larger arrays presents challenges, including precise control of trap separations and minimizing cross-talk. Future directions include the use of qudits and synthetic dimensions to expand the capabilities of quantum simulation and computation. Enhancing interaction strengths through techniques such as Rydberg-mediated interactions and exploring different molecular species offer new opportunities for quantum technologies. The field of ultracold molecules is rapidly advancing, with potential applications in quantum simulation, computation, and precision measurement.Ultracold molecules confined in optical lattices or tweezer traps offer promising platforms for quantum simulation and quantum computation. These molecules possess a large number of stable states with long coherence times, enabling precise control over their internal and external states. They can be prepared in desired states with high fidelity and are capable of generating long-range dipole-dipole interactions, which are essential for entanglement and many-body quantum states. The review discusses recent advances and challenges in this field, highlighting the potential of ultracold molecules for quantum simulation and computation. Molecules can be used to encode spin or qubit states in their rotational levels, allowing for the simulation of spin models and quantum information processing. Theoretical models, such as the dipolar XXZ model, demonstrate the potential for studying various quantum phases and interactions. Experimental progress includes the observation of spin-exchange interactions and the implementation of quantum gates using dipolar spin-exchange interactions. These experiments have shown that even low lattice fillings can exhibit dipolar interactions, paving the way for the study of many-body dynamics in disordered systems. Challenges include suppressing losses in molecular systems and achieving high fillings in optical lattices. Techniques such as shielding and dynamic decoupling have been employed to mitigate these issues. Additionally, the development of quantum gas microscopes has enabled site-resolved measurements of spin dynamics, providing insights into the anisotropy of dipolar interactions. For quantum computation, molecules provide stable qubits with long coherence times and the ability to generate entanglement through dipolar interactions. Recent experiments have demonstrated deterministic entanglement of molecule pairs using spin-exchange interactions, achieving high fidelity. Scaling up these systems to larger arrays presents challenges, including precise control of trap separations and minimizing cross-talk. Future directions include the use of qudits and synthetic dimensions to expand the capabilities of quantum simulation and computation. Enhancing interaction strengths through techniques such as Rydberg-mediated interactions and exploring different molecular species offer new opportunities for quantum technologies. The field of ultracold molecules is rapidly advancing, with potential applications in quantum simulation, computation, and precision measurement.