With the rapid development of high power laser, laser welding has been widely used in many fields including manufacturing, metallurgy, automobile, biomedicine, electronics, aerospace etc. Because of its outstanding advantages, such as high energy density, small weld size, easy automation. Combining the two heat sources of laser and arc for welding can achieve excellent results due to the synergistic effect. Laser welding is a complicated physical and chemical metallurgical process, involving the laser beam and molten pool, keyholes and materials melting, evaporation and multiple physical process. Process monitoring and quality control are important content of research and development in the field of laser welding, which is the premise to obtain fine weld with high quality. Numerical simulation technology can describe many complex physical phenomena in welding process, which is very important to predict weld forming and quality and clarify the underline mechanism. In this paper, the research progress of process monitoring, quality control and autonomous intelligent design of laser and laser-arc hybrid welding based on numerical simulation were reviewed, and the research hotspots and development trends of laser welding in the future are predicted.