Fog computing is a decentralized computing infrastructure that processes data at or near its source, reducing latency and bandwidth usage. This technology is gaining traction in healthcare due to its potential to enhance real-time data processing and decision-making capabilities in critical medical scenarios. A systematic review of existing literature on fog computing in healthcare was conducted. The review included searches in major databases such as PubMed, IEEE Xplore, Scopus, and Google Scholar. The search terms used were "fog computing in healthcare," "real-time diagnostics and fog computing," "continuous patient monitoring fog computing," "predictive analytics fog computing," "interoperability in fog computing healthcare," "scalability issues fog computing healthcare," and "security challenges fog computing healthcare." Articles published between 2010 and 2023 were considered. Inclusion criteria encompassed peer-reviewed articles, conference papers, and review articles focusing on the applications of fog computing in healthcare. Exclusion criteria were articles not available in English, those not related to healthcare applications, and those lacking empirical data. Data extraction focused on the applications of fog computing in real-time diagnostics, continuous monitoring, predictive analytics, and the identified challenges of interoperability, scalability, and security. Fog computing significantly enhances diagnostic capabilities by facilitating real-time data analysis, crucial for urgent diagnostics such as stroke detection, by processing data closer to its source. It also improves monitoring during surgeries by enabling real-time processing of vital signs and physiological parameters, thereby enhancing patient safety. In chronic disease management, continuous data collection and analysis through wearable devices allow for proactive disease management and timely adjustments to treatment plans. Additionally, fog computing supports telemedicine by enabling real-time communication between remote specialists and patients, thereby improving access to specialist care in underserved regions. Fog computing offers transformative potential in healthcare, improving diagnostic precision, patient monitoring, and personalized treatment. Addressing the challenges of interoperability, scalability, and security will be crucial for fully realizing the benefits of fog computing in healthcare, leading to a more connected and efficient healthcare environment.