Thermal photodetectors rely on thermally sensitive materials to convert the heat generated from incoming light to an electrical signal and are used in, for example, focal plane arrays and for room-temperature, high-photon-flux applications. However, the theory for thermal detectors was initially developed before nanophotonic engineering and, thus, typically assume the integrated absorbers are blackened or have a flat spectral response. Here we discuss recent developments in nanophotonics and metamaterials that have allowed for the creation of spectrally selective absorbers capable of suppressing undesired thermal emission and increasing the potential sensitivity of thermal photodetectors. Furthermore, the subwavelength features of nanophotonic or metamaterial absorbers decrease the amount of material required for absorption, which reduces the detector's thermal capacitance while increasing its response time and sensitivity. The ideal thermal and noise dynamics are derived for both spectrally selective and unselective thermal detectors, revealing exciting opportunities for future thermal photodetectors with increased sensitivities and response times and decreased noise floors.