Magnetic resonance imaging (MRI) has several advantages over other medical imaging modalities, including high contrast among different soft tissues, relatively high spatial resolution across the entire field of view and multi-spectral characteristics. Hence, it has been widely used in quantitative brain imaging studies. Quantitative volumetric measurement and three-dimensional visualization of brain tissues are helpful for pathological evolution analyses, where image segmentation plays an important role. However, MR images suffer from several major artifacts, including intensity inhomogeneity, noise, partial volume effect and low contrast, which makes MR segmentation remain a challenging topic. Therefore, this paper reviews brain MR image segmentation based on fuzzy clustering model from seven aspects, i.e., the determination of cluster number, the initialization of model, the robustness to noise, the estimation of intensity inhomogeneity and partial volume, the uncertainty description of data and the model extension. Limitations existing in the available methods are analyzed, and problems in further research are discussed as well.