Abstract: We briefly review the progress in laser－driven electron acceleration in vacuum. The dynamical characteristics and physical mechanisms of the laser－induced capture and acceleration scenario (CAS) are introduced. The physical mechanism is that the diffraction effect of the focused laser beam leads to slowing down of the effective wave phase velocity along the captured electron trajectory, such that the electron can be trapped in the acceleration phase of the wave for a longer time and thus gain significant energy from the field. The phase space of the incident electron momenta required by CAS is not small and is readily achievable in experiments. Furthermore, the optimum incident momentum is not very sensitive to the laser intensity, which is around 10—20 MeV. Our study also shows that the required laser intensity for CAS to emerge is extremely high. The electron energy gain increases sharply after entering the CAS regime. In addition, the vacuum ponderomotive laser acceleration and vacuum acceleration by the laser plus stationary magnetic field are addressed.