Antarctica provides a unique environment for astronomers to practice their trade. The cold, dry and stable air found above the high Antarctic plateau, as well as the pure ice below, offers new opportunities for the conduct of observational astronomy across both the photon and the particle spectrum. The summits of the Antarctic plateau provide the best seeing conditions, the darkest skies and the most transparent atmosphere of any earth-based observing site. Astronomical activities are now underway at four plateau sites: the Amundsen-Scott South Pole Station, Concordia Station at Dome C, Kunlun Station at Dome A and Fuji Station at Dome F, in addition to long duration ballooning from the coastal station of McMurdo, at stations run by the USA, France/Italy, China, Japan and the USA, respectively. The astronomy conducted from Antarctica includes optical, infrared, terahertz and sub-millimetre astronomy, measurements of cosmic microwave background anisotropies, solar astronomy, as well as high energy astrophysics involving the measurement of cosmic rays, gamma rays and neutrinos. Antarctica is also the richest source of meteorites on our planet. An extensive range of site testing measurements have been made over the high plateau sites. In this article, we summarise the facets of Antarctica that are driving developments in astronomy there, and review the results of the site testing experiments undertaken to quantify those characteristics of the Antarctic plateau relevant for astronomical observation. We also outline the historical development of the astronomy on the continent, and then review the principal scientific results to have emerged over the past three decades of activity in the discipline. These range from determination of the dominant frequencies of the 5 min solar oscillation in 1979 to the highest angular scale measurements yet made of the power spectrum of the CMBR anisotropies in 2010. They span through infrared views of the galactic ecology in star formation complexes in 1999, the first clear demonstration that the Universe was flat in 2000, the first detection of polarization in the CMBR in 2002, the mapping of the warm molecular gas across the ~ 300 pc extent of the Central Molecular Zone of our Galaxy in 2003, the measurement of cosmic neutrinos in 2005, and imaging of the thermal Sunyaev Zel’dovich effect in galaxy clusters in 2008. This review also discusses how science is conducted in Antarctica, and in particular the difficulties, as well as the advantages, faced by astronomers seeking to bring their experiments there. It also reviews some of the political issues that will be encountered, both at national and international level. Finally, the review discusses where Antarctic astronomy may be heading in the coming decade, in particular plans for infrared and terahertz astronomy, including the new facilities being considered for these wavebands at the high plateau stations.