In recent years, Fourier Single-Pixel Imaging (FSPI) technology has become a promising choice among the base-scanning Single-Pixel Imaging (SPI) methods due to its balance of high efficiency and high quality. This technology samples the target by projecting Fourier basis illumination patterns and achieves precise reconstruction from one-dimensional data to two-dimensional images with the help of efficient reconstruction algorithms. The FSPI technology does not rely on traditional array detectors and complex imaging systems, which doesn’t only reduce the hardware requirements for optical imaging but also broadens the range of applications, especially demonstrating significant advantages in resource-constrained or complex environmental scenarios. Therefore, research on the FSPI technology in the field of computational optical imaging holds important scientific value and application prospects. Research on the FSPI technology contains some key aspects, such as light field modulation, path optimization, reconstruction algorithms, and application scenarios. In light field modulation, the spatial dithering strategy converts Fourier grayscale illumination fields into binary illumination fields, leveraging the high-speed modulation capabilities of spatial light modulators, but this approach sacrifices image spatial resolution, affecting reconstruction quality and clarity. Although the signal dithering strategy improves the modulation rate, it does not fully match the modulation rate of the spatial light modulator to some extents. As for the path optimization, traditional sampling paths can quickly recover targets and maintain good image quality, but their adaptability to different scenes is limited. Sparse sampling methods, based on signal sparsity, reduce the number of sampling points to lower data acquisition costs while retaining sufficient information for effective reconstruction; however, these methods often require prior knowledge and have high complexity. Adaptive sampling strategies offer targeted solutions by dynamically adjusting the position and density of sampling points to optimize imaging performance. Combining adaptive sampling with deep learning is an effective approach that can further optimize sampling strategies, however, it requires high pre-training costs and potentially suboptimal performance in different imaging systems. In reconstruction algorithms, Fourier inversion demonstrates robustness under specific noise conditions but may degrade image quality in practical environments, such as atmospheric turbulence. Second-order correlation imaging, which reconstructs scenes through statistical averaging, shows good anti-scattering performance but has slightly lower imaging efficiency. Compressed sensing algorithms use signal sparsity to reduce sampling rates, but their high computational complexity and time costs are still challenging. Deep learning methods significantly enhance imaging quality at low sampling rates but require large datasets for training, and discrepancies between training and real-world environments can affect overall accuracy. The FSPI technology has shown significant potential and great value in applications such as 3D imaging, edge detection, and scattering imaging, providing innovative solutions and new directions for future imaging technology developments. With its unique imaging principles and advantages, the FSPI technology plays an important role in many fields. However, there are still many unresolved problems and challenges. Future researches can focus on optimizing imaging algorithms, improving system stability, and expanding the range of applications. In particular, advances in adaptive light modulation and real-time processing will further enhance the capabilities of FSPI technology in complex and realistic imaging scenarios, thus promoting its transformation from theoretical research to practical applications.