Single-pixel imaging reproduces scene images by modulating the light field to measure the intensity response of the scene with a single-pixel detector. Compared with traditional imaging techniques that rely on arrays of detectors to capture image information, single-pixel imaging excels in low-cost, broad-spectrum, and application-specific scenes. This technique is a novel imaging approach that shifts from the physical to the computational domain; hence, many studies are exploring efficient computational approaches. Owing to the powerful learning capability of neural networks in the computational domain, deep learning techniques have been extensively employed in single-pixel imaging and have made remarkable progress. In this paper, deep learning single-pixel imaging is categorized into three modes: data-driven, physical-driven, and hybrid-driven modes. Within each mode, neural networks are further categorized as "image-to-image" and "measurements-to-image" imaging methods. The basic theories and typical cases of single-pixel imaging methods based on deep learning are reviewed from six perspectives, and the advantages and shortcomings of each method are discussed. Finally, single-pixel imaging methods based on deep learning are summarized and discussed, and promising applications include hyperspectral imaging, transient observation, and target detection.