Owing to its scarce resources and excellent optical and physical properties, germanium is widely used in fiber-optic systems, infrared optical systems, electronic and solar energy applications, detectors, and other high-technology fields. It is an important functional and structural material which is needed in strategic industries. Two main methods of single crystal growth in germanium, Czochralski method(CZ)and vertical gradient freeze method(VGF), were briefly introduced. Technical parameters such as the method of germanium crystal growth, diameter and resistivity of germanium in popular germanium material-producing enterprises at home and abroad were analyzed and compared. Based on the properties of different single-crystal materials, the application fields and development status of germanium single crystals for infrared optics, germanium single crystal for solar cells, and high-purity germanium single crystal were analyzed.