Abstract: As the generalized Fourier transform (FT), fractional Fourier transform (FRFT) can reveal the properties of time-varying signal in time and frequency domain. By rotating the time-frequency plane, FRFT is more suitable for non-stationary signal processing and can overcome disadvantages of the cross-term interference and low resolution using traditional time-frequency analysis methods. Linear frequency modulation (LFM) signal can be regarded as the first order approximation of radar echo from moving target and hence it has great superiority in the moving target detection based on FRFT. In this paper, detection and estimation of LFM signal, determination methods of the best transform angle, et al., are firstly reviewed with the principle and characteristic of FRFT. Then, applications of FRFT in moving target detection and recognition are introduced from the following aspects: high speed weak target detection, SAR imaging and moving target detection, antiradiation missile (ARM) detection, sea target detection and radar signal recognition, et al.. In the end, future research interests are pointed out according to the problems of present study.