Isotopes, variants of elements distinguished by their neutron number, have important applications for medicine and fundamental science. This review explores the historical challenges and new technologies for enriching and detecting isotopes. We motivate the work by challenges posed by three of history’s greatest scientists: James Clerk Maxwell’s thought experiment on thermodynamics, Ernest Rutherford’s practical dilemma in radiochemistry, and Albert Einstein’s questions about the probabilistic nature of quantum mechanics. The journey to meet these challenges has catalyzed the development of innovative techniques for isotope separation. These advancements can mitigate the worldwide crisis in the supply of enriched isotopes. We then explore the expected impact of these new technologies on medicine, which include radioisotopes for cancer therapy and stable isotopes as tracers for metabolism. We explain the importance of developing scalable techniques for isotope detection and how it can help with early detection of certain diseases. Finally, we turn to basic science, outlining proposed new tests of quantum mechanics that utilize radioactive atomic clocks to probe the fundamental nature of determinism and distinguishability of atoms.