Ghost imaging (GI) is a novel imaging technique which is different from conventional imaging techniques, which extracts image information via high-order correlation of light-field fluctuations. In recent years, compared with conventional imaging techniques, GI has some advantages such as high sensitivity, super-resolution ability and anti-scattering,which make it widely studied in remote sensing, multi-spectral imaging, thermal X-ray diffraction imaging, and other fields. With these developments, mathematical theory and methods play a more prominent role in GI. For example, based on compressed sensing (CS) theory, we can optimize the sampling mode of GI system, design the algorithm of image reconstruction and analyze the quality of image reconstruction. In this paper, we discuss a few interesting mathematical problems in GI, including preconditioning, optimization of light fields, and phase retrieval. Studying these problems can be useful for enriching the theory of GI and promoting its practical applications.