The retrieval algorithm for the High Resolution Dynamics Limb Sounder (HIRDLS) instrument onboard NASA’s Earth Observing System (EOS) Aura satellite is presented. The algorithm is based on optimal estimation theory, using a modified Levenberg-Marquardt approach for the iterative solution. Overview of the retrieval scheme, convergence criteria, and the forward models is given. Treatments of clouds and aerosols as well as line-of-sight gradients in temperature are described. The retrievals are characterized by high vertical resolution of 1 km and negligible a priori contribution for all products in regions of high signal-to-noise ratio (SNR) (most of the retrieval ranges). It is shown that these characteristics hold for all latitudes along a HIRDLS orbit. The weighting functions are narrow and show good sensitivity to temperature or gas perturbations in regions of high SNR. The retrieval error predicted by the algorithm consists of radiometric noise, pointing jitter error, smoothing error, and forward model error. For temperature, these components are shown for a midlatitude profile as well as for a full orbit. The predicted temperature error varies from 0.5 K to 0.8 K from the upper troposphere to the stratopause region, consistent with the empirical estimates given by Gille et al. (2008). For O3 and HNO3, the predicted errors and their useful pressure ranges are, respectively, 10–5% from 50 to 1 hPa and 5–10% from 100 to 10 hPa. These results are based on version V004 of the retrieved data, released in August 2008 to the Goddard Earth Sciences Data and Information