Abstract The detectors in the Mid-Infrared Instrument (MIRI) of the James Webb Space Telescope (JWST) are arsenic-doped silicon impurity band conduction (Si:As IBC) devices and are direct descendants of the Spitzer IRAC long wavelength arrays (channels 3 and 4). With appropriate data processing, they can provide excellent performance. In this paper we discuss the various non-ideal behaviors of these detectors that need to be addressed to realize their potential. We have developed a set of algorithms toward this goal, building on experience with previous similar detector arrays. The MIRI-specific stage 1 pipeline algorithms, of a three stage JWST calibration pipeline, were developed using pre-flight tests on the flight detectors and flight spares and have been refined using flight data. This paper describes these algorithms, which are included in the first stage of the JWST Calibration Pipeline for the MIRI instrument.