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Quantum sensing and metrology use coherent superposition states of quantum systems to detect and measure physical effects of interest. Their sensitivity is typically limited by the standard quantum limit, which bounds the achievable precision in measurements involving nominally identical but uncorrelated quantum systems. Fully quantum metrology involves entanglement in an array of quantum systems, enabling uncertainty reduction below the standard quantum limit. Although ultracold atoms have been widely used for applications such as atomic clocks or gravitational sensors, molecules show higher sensitivity to many interesting phenomena, including the existence of new, symmetry-violating forces mediated by massive particles. Recent advancements in molecular cooling, trapping and control techniques have enabled the use of molecules for quantum sensing and metrology. This Review describes these advancements and explores the potential of the rich internal structure and enhanced coupling strengths of molecules to probe fundamental physics and drive progress in the field. 

Molecules containing short-lived, radioactive nuclei are uniquely positioned to enable a wide range of scientific discoveries in the areas of fundamental symmetries, astrophysics, nuclear structure, and chemistry. Recent advances in the ability to create, cool, and control complex molecules down to the quantum level, along with recent and upcoming advances in radioactive species production at several facilities around the world, create a compelling opportunity to coordinate and combine these efforts to bring precision measurement and control to molecules containing extreme nuclei. In this manuscript, we review the scientific case for studying radioactive molecules, discuss recent atomic, molecular, nuclear, astrophysical, and chemical advances which provide the foundation for their study, describe the facilities where these species are and will be produced, and provide an outlook for the future of this nascent field.