Phantoms are used to validate diagnostic imaging methods or improve the skills of medical professionals. For instance, they allow conducting an unlimited number of imaging studies during medical training, assessing image quality, optimizing radiation dose, and testing novel techniques and equipment. Researchers in breast imaging use anthropomorphic models to validate, assess, and optimize new methods for diagnosing breast diseases. Such models also facilitate control over the quality of diagnostic systems, help optimize clinical protocols, and improve image reconstruction algorithms. Realistic simulation of the breast tissue is essential to address the challenges of advancing X-ray mammary gland studies. The review aimed to describe phantoms currently available for diagnostic imaging and the way they were fabricated. In this literature review, PubMed, eLIBRARY, and Google Scholar databases were screened for relevant articles. Thus, 72 articles and 13 conference papers were included. The study two major types of breast phantoms: computational and physical. Specifically, computational phantoms are classified into subgroups depending on the data they use. These include mathematical models, tissue samples, and medical images of the breast. The classification of the physical phantoms is based on their manufacturing process: casting silicone-like substances, 3D printing with resins and plastics, or printing on paper using X-ray contrast ink. Computational phantoms are generally advantageous with respect to versatility, efficiency, precision, and safety and allow the generation of large amounts of virtual data. Physical phantoms provide the most realistic diagnostic images without the need for a patient and allow performing an unlimited number of radiological studies.