Three-dimensional (3D) models have led to a paradigm shift in disease modeling in vitro, particularly for cancer. The past decade has seen a phenomenal increase in the development of 3D models for various types of cancers with a focus on studying stemness, invasive behavior, angiogenesis, and chemoresistance of cancer cells, as well as contributions of its stroma, which has expanded our understanding of these processes. Cancer biology is moving into exploring the emerging hallmarks of cancer, such as inflammation, immune evasion, and reprogramming of energy metabolism. Studies into these emerging concepts have provided novel targets and treatment options such as antitumor immunotherapy. However, 3D models that can investigate the emerging hallmarks are few and underexplored. As commonly used immunocompromised mice and syngenic mice cannot accurately mimic human immunology, stromal interactions, and metabolism and require the use of prohibitively expensive humanized mice, there is tremendous scope to develop authentic 3D tumor models in these areas. Taking the specific case of breast cancer, we discuss the currently available 3D models, their applications to mimic signaling in cancer, tumor–stroma interactions, drug responses, and assessment of drug delivery systems and therapies. We discuss the lacunae in the development of 3D tumor models for the emerging hallmarks of cancer, for lesser-explored forms of breast cancer, and provide insights to develop such models. We discuss how the next generation of 3D models can provide a better mimic of human cancer modeling compared to xenograft models and the scope toward preclinical models and precision medicine.