Robust and accurate fat suppression is highly desirable in breast magnetic resonance imaging (MRI) because it can considerably improve the image quality and lesion conspicuity. However, fat suppression is also more challenging in the breast compared with other regions in the body. Technical advances have been made over time to make fat suppression more efficient and reliable. Combined with other innovations, breast MRI continues to be the most sensitive and comprehensive diagnostic modality in the detection and evaluation of breast lesions. This review offers a critical comparison of various fat suppression techniques in breast MRI including spectral-selective excitation and saturation techniques based on the chemical shift difference between fat and water, the inversion recovery techniques based on the T1 relaxation time difference, the hybrid spectral-selective inversion recovery techniques, and the new Dixon fat and water separation techniques based on the phase difference between fat and water signal at different echo times. This review will also cover less frequently used techniques such as slice-selective gradient reversal. For each fat suppression technique in breast MRI, a detailed explanation of the technical principle, the advantages and disadvantages, the approaches for optimization as well as the clinical examples are included. The additional challenges of fat suppression in breast MRI at higher field strength and in the presence of metallic and silicone implants are also discussed.