Today, adaptive optics (AO) is installed on all very large astronomical telescopes. It allows to overcome the limitation in angular resolution imposed on large ground-based telescopes by the atmospheric turbulence perturbations. This review paper presents the state of the art of the field for astronomical applications. It gives the principles of AO and describes its main components which are the deformable mirrors, the wavefront sensors and the control algorithms. The paper also presents the main recent achievements and ongoing projects. First, for the direct imaging of extra-solar planets by extreme AO and coronography, taking as example the SPHERE instrument. Then to solve the problem of the very limited sky coverage by using laser guide star and to extend the AO correction beyond the isoplanatic patch. Thus, the various laser-assisted tomographic AO concepts are presented with examples of each realization as for the laser tomography AO, the multi-conjugate AO and the multi-object AO. Finally, the challenges of the new generation of giant telescopes are discussed at the end of the paper with a particular focus on the European Extremely Large Telescope (ELT) project.