Due to be launched in late 2021, the Imaging X-Ray Polarimetry Explorer (IXPE) is a NASA Small Explorer mission designed to perform polarization measurements in the 2-8 keV band, complemented with imaging, spectroscopy and timing capabilities. At the heart of the focal plane is a set of three polarization-sensitive Gas Pixel Detectors (GPD), each based on a custom ASIC acting as a charge-collecting anode. In this paper we shall review the design, manufacturing, and test of the IXPE focal-plane detectors, with particular emphasis on the connection between the science drivers, the performance metrics and the operational aspects. We shall present a thorough characterization of the GPDs in terms of effective noise, trigger efficiency, dead time, uniformity of response, and spectral and polarimetric performance. In addition, we shall discuss in detail a number of instrumental effects that are relevant for high-level science analysis -- particularly as far as the response to unpolarized radiation and the stability in time are concerned.