Much can be learned from studying the concentrations of the ubiquitous long-lived radioactive isotopes. W. Libby and coworkers first demonstrated in 1949 that trace analysis of carbon-14 (¹⁴C; half-life = 5730 years, isotopic abundance ~1 × 10⁻¹²) can be used for archeological dating. Since then, two well-established methods, low-level counting and accelerator mass spectrometry, have been used to analyze many different trace isotopes and to extract valuable information encoded in the production, transport, and decay processes of these isotopes. The impact of ultrasensitive trace-isotope analysis has reached a wide range of scientific and technological fields.