The current and next generation satellite infrared sensors such as AIRS, IASI, CrIS, and HES all have one thing in common: large number of spectral channels. In order to fully utilize the information content of these sensors, a large number of Radiative Transfer (RT) calculations through the inhomogeneous atmosphere are needed. It is also computationally intensive to invert atmospheric and surface properties using all the channels. Usually, only subsets of channels are used to perform physical inversions for atmospheric profiles. We will explore ways to speed up RT calculations and inversions and test the algorithms using data collected by the National Polar-orbiting Operational Environmental Satellite System (NPOESS) Airborne Sounding Testbed (NAST) and by the Infrared Atmospheric Sounding Interferometer (IASI) instrument. We will describe a retrieval algorithm using a Principal Component-based Radiative Transfer Model (PCRTM) for generating atmospheric temperature/moisture/ozone profiles and surface properties (such as surface skin temperature and surface emissivities). The retrieval algorithm performs both the radiative transfer calculations and inversions in the Principal Component (PC) domain. The inversion algorithm is based on a non-linear Levenberg-Marquardt method with climatology covariance matrices and a priori information as constraints. One advantage of this approach is that it uses all information content from the ultraspectral data so that the retrieval is less sensitive to instrument noise and eliminates the need for selecting a sub-set of the channels. We will also use data collected during the Joint Airborne IASI Validation Experiment (JAIVEx) field campaign to validate the algorithm and IASI retrievals.