Our understanding of stellar evolution depends on knowing beta-decay rates and reaction cross sections for a wide range of nuclear capture reactions. Direct laboratory measurements of important stellar reaction rates are hindered by low cross sections and, in some cases, the need for radioactive targets. Indirect techniques have been developed to determine reaction rates for systems that are particularly difficult to measure in a direct experiment. One of the indirect techniques involves measurements of Asymptotic Normalization Coefficients (ANCs) which determine the direct-capture contribution to a capture reaction. Also ANCs can be used to understand the role of subthreshold states in stellar capture. This essay gives an introduction to ANCs and describes how they are used in nuclear astrophysics. Examples are given of measurements which have been carried out with both stable and radioactive beams.