The vortex beam can carry orbital angular momentum (OAM), which is associated with the spiral wavefront structure. The vortex beam has attracted a widespread attention due to its capability to significantly increase the transmission capacity and the spectral efficiency of the communication systems without the bandwidth increase. However, the turbulence in free space will cause the distortion on the spiral wavefront, resulting in the inter-mode crosstalk and the received power reduction, that degrade the communication systems’ performance. Adaptive optics is one of the effective methods to correct the distortion. The basic algorithms in adaptive optics for wavefront correction was reviewed, such as, Shack-Hartmann (SH), Stochastic-Parallel-Gradient-Descent (SPGD) and Gerchberg-Saxton (GS) algorithm, and the application of deep learning in wavefront correction was presented. At last, the authors' research work on the wavefront correction in underwater environment was introduced.