Recent technological and clinical advancements of both respiratory-correlated (RC) and time-resolved (TR) four-dimensional magnetic resonance imaging (4DMRI) techniques are reviewed in light of tumor/organ motion simulation, monitoring, and assessment in radiotherapy. For radiotherapy of thoracic and abdominal cancer, respiratory-induced tumor motion, and motion variation due to breathing irregularities are the major uncertainties in treatment. RC-4DMRI is developed to assess tumor motion for treatment planning, whereas TR-4DMRI is developed to assess both motion and motion variation for treatment planning, delivery and assessment. RC-4DMRI is reconstructed to provide one-breathing-cycle motion, similar to 4D computed tomography (4DCT), the current clinical standard, but with higher soft-tissue contrast, no ionizing radiation, and less binning artifacts due to the use of an internal respiratory surrogate. Recent studies have shown that its spatial resolution has reached or exceeded that of 4DCT and scanning time becomes clinically acceptable. TR-4DMRI is recently developed with an adequate spatiotemporal resolution to assess tumor motion and motion variations for treatment simulation, delivery and assessment. The super-resolution approach is most promising since it can image any organ/body motion, whereas RC-4D MRI are limited to resolve only respiration-induced motion and some TR-4DMRI approaches may more or less depend on RC-4DMRI. TR-4DMRI provides multi-breath motion data that are useful not only in MR-guided radiotherapy but also for building a patient-specific motion model to guide radiotherapy treatment using an non-MR-equipped linear accelerator. Based on 4DMRI motion data, motion-corrected dynamic contrast imaging and diffusion-weighted imaging have also been reported, aiming to facilitate tumor delineation for more accurate radiotherapy targeting. Both RC- and TR-4DMRI have been evaluated for potential clinical applications, such as delineation of tumor volumes, where sufficiently high spatial resolution and large field-of-view are required. The 4DMRI techniques are promising to play a role in motion assessment in radiotherapy treatment planning, delivery, assessment, and adaptation.