High resolution observations of the Sun are of key importance in understanding fundamental astrophysical processes. Adaptive optics (AO) is an important tool that allows solar astronomers to achieve diffraction limited observations from existing ground based telescopes. AO is also a key technology required for a future 4m-class Advanced Solar Telescope (AST) that the international community of solar astronomers is planning to build. The history of the development of solar AO is reviewed and results from recent successful demonstrations of solar AO systems are presented. The main difference between solar AO and night time AO is the different, and more elaborate wavefront sensing technique that has to be applied in order to measure wavefront aberrations using solar granulation as a target. Different approaches to this problem are discussed. Multi-conjugate AO has been proposed as a technique to achieve diffraction limited resolution over a field-of-view (FOV) significantly larger than the isoplanatic patch. The Sun is an ideal object for the development and application of MCAO.