MRI-linear accelerator (MR-linac) devices have been introduced into clinical practice in recent years and have enabled MR-guided adaptive radiation therapy (MRgART). However, by accounting for anatomical changes throughout radiation therapy (RT) and delivering different treatment plans at each fraction, adaptive radiation therapy (ART) highlights several challenges in terms of calculating the total delivered dose. Dose accumulation strategies-which typically involve deformable image registration between planning images, deformable dose mapping, and voxel-wise dose summation-can be employed for ART to estimate the delivered dose. In MRgART, plan adaptation on MRI instead of CT necessitates additional considerations in the dose accumulation process because MRI pixel values do not contain the quantitative information used for dose calculation. In this review, we discuss considerations for dose accumulation specific to MRgART and in relation to current MR-linac clinical workflows. We present a general dose accumulation framework for MRgART and discuss relevant quality assurance criteria. Finally, we highlight the clinical importance of dose accumulation in the ART era as well as the possible ways in which dose accumulation can transform clinical practice and improve our ability to deliver personalized RT.