In breast cancer research, diverse data types and formats, such as radiological images, clinical records, histological data, and expression analysis, are employed. Given the intricate nature of natural phenomena, relying on the features of a single modality is seldom sufficient for comprehensive analysis. Therefore, it is possible to guarantee medical relevance and achieve improved clinical outcomes by combining several modalities. The presen study carefully maps and reviews 47 primary articles from six well-known digital libraries that were published between 2018 and 2023 for breast cancer classification based on multimodal deep learning fusion (MDLF) techniques. This systematic literature review encompasses various aspects, including the medical modalities combined, the datasets utilized in these studies, the techniques, models, and architectures used in MDLF and it also discusses the advantages and limitations of each approach. The analysis of selected papers has revealed a compelling trend: the emergence of new modalities and combinations that were previously unexplored in the context of breast cancer classification. This exploration has not only expanded the scope of predictive models but also introduced fresh perspectives for addressing diverse targets, ranging from screening to diagnosis and prognosis. The practical advantages of MDLF are evident in its ability to enhance the predictive capabilities of machine learning models, resulting in improved accuracy across diverse applications. The prevalence of deep learning models underscores their success in autonomously discerning complex patterns, offering a substantial departure from traditional machine learning approaches. Furthermore, the paper explores the challenges and future directions in this field, including the need for larger datasets, the use of ensemble learning methods, and the interpretation of multimodal models.