In the era of precision medicine, increasing importance is given to machine learning (ML) applications. In breast cancer, advanced analyses, such as the radiomic process, characterise tumours and predict therapy responses. Breast magnetic resonance imaging (MRI) plays a key role in screening, staging, and treatment monitoring. Lesion segmentation on MRI is essential both to assess tumour growth and as a baseline for radiomic feature extraction. Manual segmentation is time-consuming and prone to inter-operator variability, limiting access to large labelled datasets and robust analyses. The use of ML for breast lesion segmentation on MRI has been investigated through a systematic review of PubMed, exploring studies published over the last 10 years. Results are compared in terms of performance, primarily using the Dice score. Early unsupervised methods achieved a mean Dice score of ∼0.75, surpassing traditional supervised methods (∼0.70). In contrast, deep learning (DL) approaches based on U-Net achieved higher average scores of 0.79. Further customised supervised DL approaches reached a mean Dice score of ∼0.83. However, there is still a gap in research on unsupervised DL techniques, which could help reduce bias and human variability. Future work may also explore multiparametric and multitechnique data, integrating more representative samples, including non-mass lesions.