Single-pixel imaging, a computational imaging technique utilizing wide-field illumination encoding and single-point detector sampling, offers a novel alternative to conventional imaging methods. However, the limited imaging quality and long imaging time limit the further development of single-pixel imaging in practical applications to some extent. Recent years have witnessed significant advancements in deep learning-driven single-pixel imaging, particularly in enhancing image quality and reconstruction speed. This paper elucidates the fundamental principles of deep learning and single-pixel imaging. We systematically categorize deep learning imaging methods and image-free sensing techniques in single-pixel imaging from a data mapping perspective. Additionally, we examine the advantages and limitations of both deep learning imaging methods and image-free sensing from an application standpoint. Furthermore, we comprehensively analyze the challenges facing deep learning in single-pixel imaging, explore potential solutions, and provide insights for future developments in this field.