Abstract: Concrete is a typical heterogeneous quasi-brittlematerial used in engineering, and its fracture process is very complex. Main progresses on the study of the fracture and fracture process of concrete are reviewed, a few numerical methods and models used to simulate the fracture process of concrete at macroscopic or mesoscopic level are discussed. At last, the mesomechanical model proposed by authors for simulating the macroscopic fracture process of concrete is briefly introduced.