Recent technological advances in the field of artificial intelligence hold promise in addressing medical challenges in breast cancer care, such as early diagnosis, cancer subtype determination and molecular profiling, prediction of lymph node metastases, and prognostication of treatment response and probability of recurrence. Radiomics is a quantitative approach to medical imaging, which aims to enhance the existing data available to clinicians by means of advanced mathematical analysis using artificial intelligence. Various published studies from different fields in imaging have highlighted the potential of radiomics to enhance clinical decision making. In this review, we describe the evolution of AI in breast imaging and its frontiers, focusing on handcrafted and deep learning radiomics. We present a typical workflow of a radiomics analysis and a practical “how-to” guide. Finally, we summarize the methodology and implementation of radiomics in breast cancer, based on the most recent scientific literature to help researchers and clinicians gain fundamental knowledge of this emerging technology. Alongside this, we discuss the current limitations of radiomics and challenges of integration into clinical practice with conceptual consistency, data curation, technical reproducibility, adequate accuracy, and clinical translation. The incorporation of radiomics with clinical, histopathological, and genomic information will enable physicians to move forward to a higher level of personalized management of patients with breast cancer.