Since the advent of single-pixel imaging and machine learning, both fields have flourished, but followed parallel tracks. Until recently, machine learning, especially deep learning, has demonstrated effectiveness in delivering high-quality solutions across various application domains of single-pixel imaging. This article comprehensively reviews the research of single-pixel imaging technology based on deep learning. From the basic principles of single-pixel imaging and deep learning, the principles and implementation methods of single-pixel imaging based on deep learning are described in detail. Then, the research status and development trend of single-pixel imaging based on deep learning in various domains are analyzed, including super-resolution single-pixel imaging, single-pixel imaging through scattering media, photon-level single-pixel imaging, optical encryption based on single-pixel imaging, color single-pixel imaging, and image-free sensing. Finally, this review explores the limitations in the ongoing research, while offers the delivering insights into prospective avenues for future research.