Recent medical applications are largely dominated by the application of Machine Learning (ML) models to assist expert decisions, leading to disruptive innovations in radiology, pathology, genomics, and hence modern healthcare systems in general. Despite the profitable usage of AI-based algorithms, these data-driven methods are facing issues such as the scarcity and privacy of user data, as well as the difficulty of institutions exchanging medical information. With insufficient data, ML is prevented from reaching its full potential, which is only possible if the database consists of the full spectrum of possible anatomies, pathologies, and input data types. To solve these issues, Federated Learning (FL) appeared as a valuable approach in the medical field, allowing patient data to stay where it is generated. Since an FL setting allows many clients to collaboratively train a model while keeping training data decentralized, it can protect privacy-sensitive medical data. However, FL is still unable to deliver all its promises and meets the more stringent requirements (e.g., latency, security) of a healthcare system based on multiple Internet of Medical Things (IoMT). For example, although no data are shared among the participants by definition in FL systems, some security risks are still present and can be considered as vulnerabilities from multiple aspects. This paper sheds light upon the emerging deployment of FL, provides a broad overview of current approaches and existing challenges, and outlines several directions of future work that are relevant to solving existing problems in federated healthcare, with a particular focus on security and privacy issues.