Blood vessel analysis is crucial for understanding tumor progression and provides insights into tumor biology, which are essential for diagnostics and treatment planning in breast cancer care. Furthermore, breast magnetic resonance imaging has the potential to visualize blood vessels within breast tissue by generating high-contrast images and detecting changes in blood flow. Accurate segmentation of blood vessels in breast MRI is vital for diagnosing, treatment planning, and monitoring breast cancer. This study aims to identify current methods for blood vessel segmentation in breast MRI. The main results show that these methods primarily use computer algorithms, with a few also employing machine learning algorithms. However, current blood vessel segmentation methods face significant challenges, such as low contrast, noise, and complex vessel geometries, which often result in undersegmentation. Researchers should explore hybrid models combining traditional, Machine Learning, and Deep Learning methods for robust, accurate vessel segmentation. Open, annotated breast MRI datasets and collaborative data quality efforts are essential to advance this field and enhance cancer patient care.