Pyroelectric infrared detectors (PIRDs) have a number of advantages over other IR sensors, including room-temperature operation, wide wavelength sensitivity, and low cost, leading to their use in many applications and a market expected to reach U.S.$68 million by 2025. Physical models that can be used to accurately predict the performances of PIRDs of different types are reviewed in detail. All polar dielectrics exhibit the pyroelectric effect, so there are many materials potentially available for use in PIRDs. Traditionally, a range of “figures-of-merit” (FoMs) are employed to aid the selection of the best material to use in a given application. These FoMs, and their utility in determining how a given pyroelectric material will behave in a PIRD, are reviewed in the light of the physical models and the availability of dielectric data, which cover the frequency ranges of greatest interest for PIRDs (0.1–100 Hz). The properties of several pyroelectric materials are reviewed, and models are derived for their dielectric properties as functions of frequency. It is concluded, first, that the availability of full-frequency dielectric data is highly desirable if accurate predictions of device performance are to be obtained from the models and that second, the FoMs have practical utility in only very limited circumstances. Thus, they must be used with considerable care and circumspection. The circumstances under which each FoM is likely to give a good prediction for utility are discussed. The properties of some recently researched pyroelectric materials, including lead-containing single crystals in the Pb[(Mg⅓Nb⅔)xTi1−x]O3 system and Na½Bi½TiO3–K½Bi½TiO3 based lead-free crystals and ceramics, are reviewed in the light of this, and their properties and potential for device applications compared with the industry-standard material, LiTaO3. It is concluded that while there is potential for significant device performance improvements by using improved materials, especially with the PMN-PT-based materials, factors such as temperature stability, uniformity, and ease-of-processing are at least as important as device performance in determining material utility. The properties reported for the new lead-free materials do not, as yet, promise a performance likely to compete with LiTaO3 for mm-scale detectors, a material that is both readily available and lead-free.