The Moderate Resolution Imaging Spectroradiometer (MODIS) and the Atmospheric Infrared Sounder (AIRS) measurements from the NASA Earth Observing System Aqua satellite enable global monitoring of the distribution of clouds during day and night. The MODIS is able to provide a high-spatial-resolution (1-5 km) cloud mask, cloud classification mask, cloud-phase mask, cloud-top pressure (CTP), and effective cloud amount during both the daytime and the nighttime, as well as cloud particle size (CPS) and cloud optical thickness (COT) at 0.55µm during the daytime. The AIRS high-spectral-resolution measurements reveal cloud properties with coarser spatial resolution (13.5 km at nadir). Combined, MODIS and AIRS provide cloud microphysical properties during both the daytime and nighttime. A fast cloudy radiative transfer model for AIRS that accounts for cloud scattering and absorption is described in this paper. One-dimensional variational (1DVAR) and minimum-residual (MR) methods are used to retrieve the CPS and COT from AIRS longwave window region (790-970 cm-1 or 10.31-12.66µm, and 1050-1130 cm-1 or 8.85-9.52µm) cloudy radiance measurements. In both 1DVAR and MR procedures, the CTP is derived from the AIRS radiances of carbon dioxide channels while the cloud-phase information is derived from the collocated MODIS 1-km phase mask for AIRS CPS and COT retrievals. In addition, the collocated 1-km MODIS cloud mask refines the AIRS cloud detection in both 1DVAR and MR procedures. The atmospheric temperature profile, moisture profile, and surface skin temperature used in the AIRS cloud retrieval processing are from the European Centre for Medium-Range Weather Forecasts forecast analysis. The results from 1DVAR are compared with the operational MODIS products and MR cloud microphysical property retrieval. A Hurricane Isabel case study shows that 1DVAR retrievals have a high correlation with either the operational MODIS cloud products or MR cloud property retrievals. 1DVAR provides an efficient way for cloud microphysical property retrieval during the daytime, and MR provides the cloud microphysical property retrievals during both the daytime and nighttime.