This article provides the necessary background for curators and specialists in art history to understand the carbon-14 dating procedure and subsequently to understand the limits of the technique. The miniature counter, developed for use at the Smithsonian (CAL), is described. The design innovations required in constructing a miniature carbon-14 counter included fabricating the counters essentially out of highly purified quartz and metals. Glass is present only in the last centimeter of the graded seal at the extremities of the legs, extending some distance from the counting chamber, which are necessary to seal in the external electrical leads. Construction was such as to permit a thorough high-temperature baking out of the detectors under vacuum. The detectors are filled to a pressure of four atmospheres with carefully purified carbon dioxide prepared by combustion of the sample being measured. Uses three cases, an Eskimo mask, the Fröbisher Bloom, and the Stavelot Triptych, to demonstrate how the method can be applied to questions of an object's history. The Grolier Codex, the Vinland Map, and the Shroud of Turin are other artifacts about which milligram sampling may provide useful information. The technique can present proof of forgery but not of authenticity. Wood, paper, leather, cloth, and bone can be dated using this technique. The advantages and limitations of the small counter over accelerators for carbon-14 measurement are discussed.