A laser plasma accelerator is a new kind of particle accelerator which has been developed in recent decades worldwide. It has a broad range of potential applications both in scientific research and in our everyday life. This paper describes the basic principles and experimental developments of both laser electron acceleration and laser ion acceleration. As a newly emerging field, laser accelerator research has seen many exciting achievements but is also confronted with many challenges. The prospects for the development and application of laser accelerators are reviewed in the conclusion.