A Principal Component-based Radiative Transfer Model (PCRTM), which can calculate TOA radiance or reflectance spectra from 50 cm^-1 to 40,000 cm^-1 (200 mm to 0.25 mm) was developed. It demonstrated very good accuracy relative to reference Line-by-Line radiative transfer models and saves orders of magnitude in computational time. The PCRTM performs radiative transfer calculation in a limited number of monochromatic wavelengths, which avoids the approximation assumptions that are made in the correlated-K method. The PCRTM model was developed for hyperspectral sensors such as AIRS, CrIS, IASI, NAST-I, SHIS, FIRST, and CLARREO-IR in the thermal IR spectral region and CLARREO-Solar, CPF, TEMPO, EMIT, OMI, and SCIAMACHY in the solar spectral region. The PCRTM's accuracy was demonstrated via RTM intercomparisons and with real satellite observations from AIRS, CrIS, IASI, SCIAMACHY, EMIT, etc. The PCRTM has been used in many satellite remote sensing applications. Examples include forward modeling in Level-2 and Level-3 retrieval algorithms, high-fidelity satellite instrument simulators and instrument performance trade studies, spectral and radiometric accuracy characterizations of satellite Level-1 data, tools for inter-satellite calibrations, tools for satellite RTM lookup table generations, and tools for generating physically based training datasets for Artificial Intelligence (AI) algorithms.