While computer vision systems often assume simple illumination models, real-world illumination is highly complex, consisting of reflected light from every direction as well as distributed and localized primary light sources. One can capture the illumination incident at a point in the real world from every direction photographically using a spherical illumination map. This paper illustrates, through analysis of photographically-acquired, high dynamic range illumination maps, that real-world illumination shares many of the statistical properties of natural images. In particular, the marginal and joint wavelet coefficient distributions, directional derivative distributions, and harmonic spectra of illumination maps resemble those documented in the natural image statistics literature. However, illumination maps differ from standard photographs in that illumination maps are statistically non-stationary and may contain localized light sources that dominate their power spectra. Our work provides a foundation for statistical models of real-world illumination that may facilitate robust estimation of shape, reflectance, and illumination from images.