Imaging at non-visible wavebands is one of the challenges in optical imaging. As a novel computational imaging technique, single-pixel imaging based on spatial light modulation is able to obtain spatial information of object via a non-spatially-resolving detector. Thus, single-pixel imaging technique is a potential approach to the challenge of imaging at non-visible wavebands. In recent years, Fourier single-pixel imaging is demonstrated to be able to offer high-quality and high-efficiency image acquisition. Since proposed in 2015, Fourier single-pixel imaging technique has been extended a series of techniques ranging from two-dimensional imaging to three-dimensional imaging, from mono-chromatic imaging to true-color imaging, from static imaging to dynamic imaging, from single-modality imaging to multi-modality imaging, and from photography to microscopy. The principle and related applications of Fourier single-pixel imaging were reviewed. Some challenging problems and prospects of the technique were also discussed.