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Atomic-resonance magnetometers with optical pumping (OPM) measure the frequency of magnetic resonance of paramagnetic atoms by methods of radio-optical spectroscopy. These instruments appeared at the beginning of the 1960s and attracted attention by their high variation sensitivity, which is independent of induction in the range below 10- 4 T. Since the 1970s, the efforts of researchers have been directed toward overcoming the gap between OPM variation sensitivity and accuracy. A number of laboratory OPMs have been created whose absolute error has been reduced to 10- 2 nT for a variation sensitivity of the same order. Similar accuracy characteristics were obtained in these instruments by substantially different methods, accompanied by a variety of design and operating features and not allowing an unconditional preference of one solution over another. A final decision can be made only on the basis of the specific application of the instrument. Various methods of precision-OPM design are compared with the aim of assisting users in selecting an optimum magnetometer.