Transfer learning refers to machine learning techniques that focus on acquiring knowledge from related tasks to improve generalization in the tasks of interest. In MRI, transfer learning is important for developing strategies that address the variation in MR images. Additionally, transfer learning is beneficial to re-utilize machine learning models that were trained to solve related tasks to the task of interest. Our goal is to identify research directions, gaps of knowledge, applications, and widely used strategies among the transfer learning approaches applied in MR brain imaging. We performed a systematic literature search for articles that applied transfer learning to MR brain imaging. We screened 433 studies and we categorized and extracted relevant information, including task type, application, and machine learning methods. Furthermore, we closely examined brain MRI-specific transfer learning approaches and other methods that tackled privacy, unseen target domains, and unlabeled data. We found 129 articles that applied transfer learning to brain MRI tasks. The most frequent applications were dementia related classification tasks and brain tumor segmentation. A majority of articles utilized transfer learning on convolutional neural networks (CNNs). Only few approaches were clearly brain MRI specific, considered privacy issues, unseen target domains or unlabeled data. We proposed a new categorization to group specific, widely-used approaches. There is an increasing interest in transfer learning within brain MRI. Public datasets have contributed to the popularity of Alzheimer's diagnostics/prognostics and tumor segmentation. 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 to other approaches.