Abstract: In recent years, the application of the theory and methods of modern statistical physics to the study of earthquakes and earthquake prediction has had significant progress, and became one of the most active interdisciplinary frontiers between physics and seismology. Developments in this field, such as the earthquake models which regard the earthquake occurrencer as a critical phenomenon,not only improved phenomenology and understanding of the physics of earthquakes but also changed some of the traditional know-how and methodology of earthquake prediction.This paper introduces recent advances in this field,with special emphasis on the key concepts and outstanding scientific problems related to the statistical physics of earthquakes.