Single-pixel imaging(SPI) as a new imaging technology with low cost of detectors and wide imaging range has wide applications in remote sensing imaging, hyperspectral imaging, and lidar detection, etc. Since SPI has a unique imaging mechanism and framework, specialized image processing algorithms need to be designed. This review, based on the development of SPI, describes the research progresses of SPI in image classification, moving object imaging, blind reconstruction, image encryption and hiding, edge detection, illumination pattern optimization, low-sampling rate image quality improvement. In addition, we briefly discuss the future directions of image processing algorithms related to SPI.