The advancement of precision radiotherapy techniques, such as volumetric modulated arc therapy (VMAT), stereotactic body radiotherapy (SBRT), and particle therapy, highlights the importance of radiotherapy in the treatment of cancer, while also posing challenges for respiratory motion management in thoracic and abdominal tumors. MRI-guided radiotherapy (MRIgRT) stands out as state-of-art real-time respiratory motion management approach owing to the non-ionizing radiation nature and superior soft-tissue contrast characteristic of MR imaging. In clinical practice, MR imaging often operates at a frequency of 4 Hz, resulting in approximately a 300 ms system latency of MRIgRT. This system latency decreases the accuracy of respiratory motion management in MRIgRT. Artificial intelligence (AI)-based respiratory motion prediction has recently emerged as a promising solution to address the system latency issues in MRIgRT, particularly for advanced contour prediction and volumetric prediction. However, implementing AI-based respiratory motion prediction faces several challenges including the collection of training datasets, the selection of prediction methods, and the formulation of complex contour and volumetric prediction problems. This review presents modeling approaches of AI-based respiratory motion prediction in MRIgRT, and provides recommendations for achieving consistent and generalizable results in this field.