Thermal effects in solid state laser media have become a bottleneck of the development towards high power for diode-pumped sold state laser. The cryogenically cooled Yb:YAG solid state laser can realize high average power and good beam quality. Its advantages including low laser threshold,high efficiency and scalable output,are summarized. The thermo-optic and spectroscopic properties of Yb:YAG crystal at lower temperatures are analyzed,which makes it possible to provide efficient laser sources with small thermal effect. Finally three different cooling methods are compared and the progress in cryogenically cooled high average power Yb:YAG laser is presented.