SummaryResearch in astronomy is undergoing a profound transformation from the study of small samples to the analysis of large‐scale digital surveys of the sky. Ever larger amounts of data and better statistical techniques are being used to address a vast range of astronomical problems, from near‐by asteroids to universe‐wide cosmology. There is a huge need for new methodology development to address petabyte‐sized datasets of images, atlases with millions of spectra, multivariate catalogues and time series with billions of objects. The focus of this article is on the analysis of light‐curves (i.e. the variation of source brightness as a function of time). A description of the importance of the problem and the techniques already being used is given. The field is ripe with many statistical and computational challenges.