Magnetic particle imaging (MPI) is an emerging molecular imaging technique with high sensitivity and temporal-spatial resolution. Image reconstruction is an important research topic in MPI, which converts an induced voltage signal into the image of superparamagnetic iron oxide particles concentration distribution. MPI reconstruction primarily involves system matrix- and x-space-based methods. In this review, we provide a detailed overview of the research status and future research trends of these two methods. In addition, we review the application of deep learning methods in MPI reconstruction and the current open sources of MPI. Finally, research opinions on MPI reconstruction are presented. We hope this review promotes the use of MPI in clinical applications.