Artificial intelligence enhances the boundaries and capabilities of medical imaging. Hence, researchers are continuously attempting to develop an efficient and automated diagnosis system to increase the accuracy and performance to diagnose the brain abnormality. Therefore, it is required that a suitable method to diagnose and classify brain-related diseases such as Alzheimer disease, cancer, dementia, etc. Magnetic resonance imaging (MRI) is a powerful imaging technique in neuroscience for studying brain images. In the past years, many brain MRI classification techniques were proposed. Machine learning and deep learning have demonstrated a wonderful performance in the classification task. In this paper, the study of various brain MRI classification techniques has been provided. The aim of this study is to help the doctors/neurologists in selection of appropriate classification method based on several parameters like accuracy, computer complexity, and low training data availability. We also analyze and compare the performance of different classification methods based on several evaluation metrics.