The Luby Transform (LT)codes is the first digital fountain codes that has practical values. LT codes can demonstrate excellent performance in noisy channels, and it has been widely applied in Free Space Optical Communications (FSO). In this article, the basic principle of LT codes is introduced, and the advantages and disadvantages of LT codes and other common encoding schemes for FSO are listed. Besides that, the progress of both domestic and foreign researches on the applications of LT codes in FSO systems is summarized. Then, the strategies for enhancing the performance of LT codes in FSO systems are elaborately described in two aspects, i.e., novel degree distributions and improved decoding schemes. Finally, the incompletions of the existing researches on LT codes are indicated, and some directions of further researches on LT codes in FSO are depicted.