Dark matter and dark energy are considered as the "two clouds of physics at the 21st century", among the frontier of fundamental physics and cosmology research. The breakthrough will significantly change our understanding of the Universe and the fundamental law of physics. Both United States and Europe have made increasing support for the research of dark matter and approved several mid-term and long-term plans of large projects. In the last several years, China has made significant progress on the detection of dark matter, in particular the development of Jinping Underground Laboratory, and the Dark Matter Particle Explorer (DAMPE) has been launched last December. DAMPEhas the potential to discover dark matter particle through indirect detection approach by observing the secondary particles from dark matter annihilation. In this article, we briefly introduce the history of dark matter concept and a summary of astronomical approaches to study dark matter.