X-ray fluorescence spectroscopy has been in use since the early days of the twentieth century, when Moseley confirmed the order of the chemical periodic table. However, fluorescence spectroscopy until recently has depended on diffraction methods to obtain sufficient resolution. Intrinsic resolution of ionization chambers, scintillation detectors, and proportional counters is inadequate for discrimination o f lines due to adjacent elements of low atomic number. The advent o f solid-state detectors, especially those using lithium-compensated silicon and low-noise electronics, has recently brought intrinsic energy resolution to the point where lines from adjacent elements as light as carbon and nitrogen can be resolved in theory; and detection of K radiation from elements as light as sodium is practical. Thus the solution to the long-standing problem of an adequate detector is at hand, and energy-dispersive spectrometers are now feasible.