The neuroimaging method of multimodal magnetic resonance imaging (MRI) can identify the changes in brain structure and function caused by Alzheimer's disease (AD) at different stages, and it is a practical method to study the mechanism of AD progression. This paper reviews the studies of methods and biomarkers for predicting AD progression based on multimodal MRI. First, different approaches for predicting AD progression are analyzed and summarized, including machine learning, deep learning, regression, and other MRI analysis methods. Then, the effective biomarkers of AD progression under structural magnetic resonance imaging, diffusion tensor imaging, functional magnetic resonance imaging, and arterial spin labeling modes of MRI are summarized. It is believed that the brain changes shown on MRI may be related to the cognitive decline in different prodrome stages of AD, which is conducive to the further realization of early intervention and prevention of AD. Finally, the deficiencies of the existing studies are analyzed in terms of data set size, data heterogeneity, processing methods, and research depth. More importantly, future research directions are proposed, including enriching data sets, simplifying biomarkers, utilizing multimodal magnetic resonance, etc. In the future, the study of AD progression by multimodal MRI will still be a challenge but also a significant research hotspot.