Spatial point processes in astronomy

We review several topics arising in astronomical research where the statistical analysis of spatial point processes plays a central role in scientific investigations. These include: the distribution of stars in the Milky Way; the distribution of galaxies in two and three dimensions; the location of clusters of photons from faint astronomical sources in detectors; the classification of objects in large multivariate databases; and the sky distribution of gamma-ray bursters. A variety of challenging methodological issues arise including anisotropic filamentary clustering, modeling of Poisson spatial processes, and weighted measures of clustering.