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Ultrafast switching speed, low power, natural quantization of magnetic flux, quantum accuracy, and low noise of cryogenic superconductor circuits enable fast and accurate data conversion between the analog and digital domains. Based on rapid single-flux quantum (RSFQ) logic, these integrated circuits are capable of achieving performance levels unattainable by any other technology. Two major classes of superconductor analog-to-digital converters (ADCs) are being developed - Nyquist sampling and oversampling converters. Complete systems with digital sampling at rates of ∼20 GHz and above have been demonstrated using low-temperature superconductor device technology. Some ADC components have also been implemented using high-temperature superconductors. Superconductor ADCs have unique applications in true digital-RF communications, broadband instrumentation, and digital sensor readout. Their designs, test results, and future development trends are reviewed.