(1) Background: Transfer learning refers to machine learning techniques that focus on acquiring knowledge from related tasks to improve generalization in the tasks of interest. In magnetic resonance imaging (MRI), transfer learning is important for developing strategies that address the variation in MR images from different imaging protocols or scanners. Additionally, transfer learning is beneficial for reutilizing machine learning models that were trained to solve different (but related) tasks to the task of interest. The aim of this review is to identify research directions, gaps in knowledge, applications, and widely used strategies among the transfer learning approaches applied in MR brain imaging; (2) Methods: We performed a systematic literature search for articles that applied transfer learning to MR brain imaging tasks. We screened 433 studies for their relevance, and we categorized and extracted relevant information, including task type, application, availability of labels, and machine learning methods. Furthermore, we closely examined brain MRI-specific transfer learning approaches and other methods that tackled issues relevant to medical imaging, including privacy, unseen target domains, and unlabeled data; (3) Results: We found 129 articles that applied transfer learning to MR brain imaging tasks. The most frequent applications were dementia-related classification tasks and brain tumor segmentation. The majority of articles utilized transfer learning techniques based on convolutional neural networks (CNNs). Only a few approaches utilized clearly brain MRI-specific methodology, and considered privacy issues, unseen target domains, or unlabeled data. We proposed a new categorization to group specific, widely-used approaches such as pretraining and fine-tuning CNNs; (4) Discussion: There is increasing interest in transfer learning for brain MRI. Well-known public datasets have clearly contributed to the popularity of Alzheimer’s diagnostics/prognostics and tumor segmentation as applications. Likewise, the availability of pretrained CNNs has promoted their utilization. Finally, the majority of the surveyed studies did not examine in detail the interpretation of their strategies after applying transfer learning, and did not compare their approach with other transfer learning approaches.