Abstract: Significant progress has been achieved in enhancing the energy and quality of electron beams since the proposal of laser wakefield acceleration by Tajima and Dawson more than 20 years ago. Breakthroughs in the generation of quasi－monoenergetic electron beams in several laboratories in 2004 spurred new interest in this type of compact accelerator. Even though its mechanism is not yet completely understood, it is believed that the so－called bubble acceleration is one of the main mechanisms. The basic principle of the laser wakefield acceleratorwill be explained briefly and wavebreaking and self－injection in the bubble regime described, including recent experimental and theoretical progress.