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Since its introduction in 2016, researchers have applied the idea of Federated Learning (FL) to several domains ranging from edge computing to banking. The technique's inherent security benefits, privacy-preserving capabilities, ease of scalability, and ability to transcend data biases have motivated researchers to use this tool on healthcare datasets. While several reviews exist detailing FL and its applications, this review focuses solely on the different applications of FL to medical imaging datasets, grouping applications by diseases, modality, and/or part of the body. This Systematic Literature review was conducted by querying and consolidating results from ArXiv, IEEE Xplorer, and PubMed. Furthermore, we provide a detailed description of FL architecture, models, descriptions of the performance achieved by FL models, and how results compare with traditional Machine Learning (ML) models. Additionally, we discuss the security benefits, highlighting two primary forms of privacy-preserving techniques, including homomorphic encryption and differential privacy. Finally, we provide some background information and context regarding where the contributions lie. The background information is organized into the following categories: architecture/setup type, data-related topics, security, and learning types. While progress has been made within the field of FL and medical imaging, much room for improvement and understanding remains, with an emphasis on security and data issues remaining the primary concerns for researchers. Therefore, improvements are constantly pushing the field forward. Finally, we highlighted the challenges in deploying FL in medical imaging applications and provided recommendations for future directions. [ABSTRACT FROM AUTHOR]