Vortex beam is a new kind of beams with helical wavefront. It has an annular intensity distribution, and with orbital angular momentum(OAM) related to the helical wavefront. The OAM state of a vortex beam can be any integer, and vortex beams with different OAM states are mutually orthogonal, which indicates the potential of enlarging the capacity of optical communications. However, when a vortex beam propagates in free space, its wavefront will be distorted by the turbulence of the atmosphere. It is necessary to study how to compensate the wavefront distortion by using adaptive optics system. In this paper, some adaptive optics correction approaches were summarized. Moreover, schemes of correcting distorted vortex beams, which were proposed by our group, were introduced. One scheme was the pre-compensation method by using the GS algorithm and a Gaussian probe beam. The other one was a phase correction method by using a Zernike polynomials-based SPGD algorithm.