Laser wakefield accelerators（LWFAs） are compact accelerators which can produce femtosecond high-energy electron beams on a much smaller scale than the conventional radiofrequency accelerators. It is attributed to their high acceleration gradient which is about 3 orders of magnitude larger than the traditional ones. The past decade has witnessed the major breakthroughs and progress in developing the laser wakfield accelerators. To achieve the LWFAs suitable for applications,more and more attention has been paid to optimize the LWFAs for high-quality electron beams. A single-staged LWFA does not favor generating controllable electron beams beyond 1 Ge V since electron injection and acceleration are coupled and cannot be independently controlled. Staged LWFAs provide a promising route to overcome this disadvantage by decoupling injection from acceleration and thus the electron-beam quality as well as the stability can be greatly improved.This paper provides an overview of the physical conceptions of the LWFA, as well as the major breakthroughs and progress in developing LWFAs from single-stage to two-stage LWFAs.