This paper documents the climatological mean features of the Atmospheric Infrared Sounder (AIRS) monthly mean tropospheric air temperature (ta, K) and specific humidity (hus, kg/kg) products as part of the Obs4MIPs project and compares them to those from NASA's Modern Era Retrospective analysis for Research and Applications (MERRA) for validation and 16 models from the fifth phase of the Coupled Model Intercomparison Project (CMIP5) for CMIP5 model evaluation. MERRA is warmer than AIRS in the free troposphere but colder in the boundary layer with differences typically less than 1 K. MERRA is also drier (~10%) than AIRS in the tropical boundary layer but wetter (~30%) in the tropical free troposphere and the extratropical troposphere. In particular, the large MERRA-AIRS specific humidity differences are mainly located in the deep convective cloudy regions indicating that the low sampling of AIRS in the cloudy regions may be the main reason for these differences. In comparison to AIRS and MERRA, the sixteen CMIP5 models can generally reproduce the climatological features of tropospheric air temperature and specific humidity well, but several noticeable biases exist. The models have a tropospheric cold bias (around 2 K), especially in the extratropical upper troposphere, and a double-ITCZ problem in the troposphere from 1000 hPa to 300 hPa, especially in the tropical Pacific. The upper-tropospheric cold bias exists in the most (13 of 16) models, and the double-ITCZ bias is found in all 16 CMIP5 models. Both biases are independent of the reference dataset used (AIRS or MERRA).