Modern spaceborne atmospheric sounders measure radiance with unprecedented resolution (spatial, spectral, and temporal) and accuracy. For example, the Atmospheric Infrared Sounder (AIRS, operational on the NASA EOS Aqua satellite since late 2002) provides a spatial resolution of approximately 15 km, a spectral resolution of ν/Δν ≈ 1200 (with 2,378 channels from 650 to 2675 cm^-1), and a radiometric accuracy on the order of ±0.2 K. Approximately 90 percent of the Earth's atmosphere is measured (in the horizontal dimension) approximately every 12 hours. The retrieval algorithms estimate the geophysical state of the atmosphere as a function of space and time from upwellling spectral radiances measured by the sensor. In this paper, we present two examples of neural-network-based atmospheric retrieval algorithms. First, we consider the retrieval of atmospheric temperature and moisture profiles (quantity as a function of altitude) from hyperspectral radiance measurements in the thermal infrared. A projected principal components (PPC) transform is used to reduce the dimensionality of and optimally extract geophysical information from the spectral radiance data, and a multilayer feed-forward neural network (NN) is subsequently used to estimate the desired geophysical profiles. This algorithm is henceforth referred to as the “PPC/NN” algorithm. The PPC/NN algorithm offers the numerical stability and efficiency of statistical methods without sacrificing the accuracy of physical, model-based methods. Second, we consider the retrieval of precipitation rate from passive microwave radiance measurements at frequencies near the oxygen and water vapor resonances at 50-60 GHz and 183.31 GHz, respectively. In this case, the models relating the precipitation rate to the radiance intensities measured by the sensor are extremely complicated and difficult to validate. The use of neural networks to empirically learn the statistical relationship between rain rate and spectral intensity obviates the need for complex and, often, inaccurate models in the retrieval algorithm.