The discovery of a new superconductor, LaFeAsO1-xFx with a superconducting critical temperature,T-c, of 26 K in 2008, has quickly renewed interest in the exploration of iron-based superconductors. More than 70 new superconductors have been discovered within several months, with the highest T-c of up to 55 K being observed in the SmFeAsO1-x compound. High T(c)s have previously only been observed in cuprates; these new iron-based superconductors have been added as second members of the high-T-c family. The crystal structure of these compounds contains an almost 2D Fe-As layer formed by FeAs4 tetrahedrons, which can be separated by an oxide or metal layer that provides extra electrons to the Fe-As layer, and the itinerant iron 3d electrons form an antiferromagnetic (AFM) order state in the undoped parent compounds at around 100-200 K. Superconductivity can be induced by carrier doping, which destroys the AFM ground state. In this Review, the most recent findings on and basic experimental facts about this class of high-T-c materials will be presented, including the various superconducting structures, the synthesis methods, the physical properties of the parent compounds, the doping methods that could produce superconductivity, pressure effects, and the prospects for this new iron-based high-T-c family.