The article reviews the advancements and challenges in using ultracold molecules for quantum simulation and quantum computation. Ultracold molecules, confined in optical lattices or tweezer traps, offer several advantages for these applications, including a large set of stable states with strong transitions, long coherence times, and controllable long-range dipole-dipole interactions (DDIs). The review highlights the theoretical considerations, such as the molecular structure and interactions, and discusses the experimental progress in creating and manipulating these molecules. It covers the development of model Hamiltonians and many-body phases, the challenges in suppressing losses, and the potential for implementing complex Hamiltonians and exploring new ultracold molecules. The article also explores the use of molecules in tweezer arrays for quantum computation, including qubit design, coherence times, and entanglement techniques. Finally, it outlines future research directions, such as controlling collisions, creating synthetic dimensions, increasing interaction strengths, and exploring different molecular species. The authors emphasize the rapid progress in the field and the potential for future developments in quantum science and technology.The article reviews the advancements and challenges in using ultracold molecules for quantum simulation and quantum computation. Ultracold molecules, confined in optical lattices or tweezer traps, offer several advantages for these applications, including a large set of stable states with strong transitions, long coherence times, and controllable long-range dipole-dipole interactions (DDIs). The review highlights the theoretical considerations, such as the molecular structure and interactions, and discusses the experimental progress in creating and manipulating these molecules. It covers the development of model Hamiltonians and many-body phases, the challenges in suppressing losses, and the potential for implementing complex Hamiltonians and exploring new ultracold molecules. The article also explores the use of molecules in tweezer arrays for quantum computation, including qubit design, coherence times, and entanglement techniques. Finally, it outlines future research directions, such as controlling collisions, creating synthetic dimensions, increasing interaction strengths, and exploring different molecular species. The authors emphasize the rapid progress in the field and the potential for future developments in quantum science and technology.