A Fourier transform spectrometer (FTS) is recognized as a highly precise analytical instrument for analyzing the constituent elements of matter in the fields of physics, chemistry, aerospace, and so on. With the emergence and development of miniaturized and portable devices in numerous scientific and technological fields, there has been an urgent need for on-chip FTSs due to their benefits of small size, portability, low energy consumption, and robustness. However, the small size of on-chip FTSs hinders the acquisition of a large optical path difference, resulting in a low resolution of the spectrometer. In addition, the sampler spacing is not sufficiently small to satisfy Nyquist's sampling theorem, directly influencing the bandwidth of the spectrometer. Therefore, studies have been performed to investigate the trade-off between the reduced size and performance of spectrometers. This paper aims to systematically review the progress in on-chip FTSs, especially in on-chip static FTSs, including spatially modulated, temporally modulated, and space-time comodulated FTSs, from the aspects of theories, implementations, and performance indicators. Finally, the paper ends with a discussion of the challenges and a view of the prospective development of this exciting field.