PURPOSE: In radiotherapy, MRI is used for target volume and organs-at-risk delineation for its superior soft-tissue contrast as compared to CT imaging. However, MRI does not provide the electron density of tissue necessary for dose calculation. Several methods of synthetic-CT (sCT) generation from MRI data have been developed for radiotherapy dose calculation. This work reviewed deep learning (DL) sCT generation methods and their associated image and dose evaluation, in the context of MRI-based dose calculation. METHODS: We searched the PubMed and ScienceDirect electronic databases from January 2010 to March 2021. For each paper, several items were screened and compiled in figures and tables. RESULTS: This review included 57 studies. The DL methods were either generator-only based (45% of the reviewed studies), or generative adversarial network (GAN) architecture and its variants (55% of the reviewed studies). The brain and pelvis were the most commonly investigated anatomical localizations (39% and 28% of the reviewed studies, respectively), and more rarely, the head-and-neck (HandN) (15%), abdomen (10%), liver (5%) or breast (3%). All the studies performed an image evaluation of sCTs with a diversity of metrics, with only 36 studies performing dosimetric evaluations of sCT. CONCLUSIONS: The median mean absolute errors were around 76 HU for the brain and HandN sCTs and 40 HU for the pelvis sCTs. For the brain, the mean dose difference between the sCT and the reference CT was <2%. For the HandN and pelvis, the mean dose difference was below 1% in most of the studies. Recent GAN architectures have advantages compared to generator-only, but no superiority was found in term of image or dose sCT uncertainties. Key challenges of DL-based sCT generation methods from MRI in radiotherapy is the management of movement for abdominal and thoracic localizations, the standardization of sCT evaluation, and the investigation of multicenter impacts.