During the past 20 years there has been a resumption of a dialogue between astronomers and statisticians. This dialogue has been fruitful and has been the origin of a new discipline that is now widely called Astrostatistics. The main tools for comparing theoretical results with observations in astronomy are statistical. However, the development of huge astronomical databases presents challenges of scale, and has initiated an active use of newly-developed statistical techniques in astronomy, notable examples being sparsity and compressed sensing.