This paper presents a survey of advanced methods for segmenting the MRI (Magnetic Resonance Imaging) image of the brain. Segmentation of the brain is a challenging task because it requires more emphasized methods to differentiate each of the regions present in the brain image. The intensity differences between the different regions in the brain MRI image are very less, making it difficult to automate the entire segmentation process. Hence, a thorough understanding of the existing segmentation algorithm is essential for accurate segmentation. The segmentation algorithms surveyed in this work are Neural Network Model, Self-Organizing Maps, Radial Basis Function, Back Propagation, Fuzzy C-Means, Deformable Models, Level Set Models, Genetic Algorithm, Differential Evolutionary Algorithm, Hybrid Clustering and Artificial Intelligence. Such a survey would be helpful for researchers working in the field of brain image segmentation. The paper discusses the complexities in the segmentation algorithm and also the challenges in segmenting the brain MRI images. The segmentation outputs and analysis of the existing literature has also been discussed. The major criteria and their advantages in the segmentation of each algorithm have been reported accordingly in the observations.