Magnetic resonance imaging (MRI) is one of the most popular techniques in brain science and is important for understanding brain function and neuropsychiatric disorders. However, the processing and analysis of MRI is not a trivial task with lots of challenges. Recently, deep learning has shown superior performance over traditional machine learning approaches in image analysis. In this survey, we give a brief review of the recent popular deep learning approaches and their applications in brain MRI analysis. Furthermore, popular brain MRI databases and deep learning tools are also introduced. The strength and weaknesses of different approaches are addressed, and challenges as well as future directions are also discussed.