Glass materials are widely used in semiconductor, micro-electromechanical system, microfluidic chip, optical communication, optical storage, and other emerging fields due to its excellent and unique physical and chemical properties. As a new non-contact machining method, laser technology can carry out high-precision and high-efficiency micro-machining on the surface and inside of glass materials, which shows great development potential in the field of glass material processing. In this paper, the basic principle and key problems of four typical laser machining glass processes: Laser etching, laser drilling, laser welding, and laser fabrication of functional structures were reviewed. And the latest research progress, technological level, and application status of laser processing of glass materials were pointed out. Laser etching includes laser direct-writing etching, laser-induced plasma-assisted ablation, and laser-induced backside wet etching; laser drilling includes far-infrared CO2 laser drilling, ultrafast laser drilling, and improved new drilling methods; laser welding includes far-infrared CO2 laser welding, nanosecond laser welding, and ultrafast laser welding; while laser fabrication of functional structures was divided into surface functional structures fabrication and internal functional structures fabrication. At the same time the advantages and disadvantages of four kinds of laser machining glass processes were summarized, and the bottleneck problems were analyzed. On this basis, the development prospect of laser processing technology for glass materials is summarized and prospected.