The integration of IoT, Fog Computing (FC), and Cloud Computing (CC) is revolutionizing healthcare by enhancing real-time monitoring, data processing, and resource management. IoT enables seamless connectivity among medical devices, facilitating real-time patient monitoring and remote healthcare services. Cloud computing provides scalable storage and computational power, ensuring efficient data management and analytics. However, latency-sensitive healthcare applications face challenges due to the centralized nature of cloud infrastructure. Fog computing mitigates these challenges by bringing computational resources closer to the data source, reducing latency, and improving response times. This chapter explores the synergy of these technologies in the smart healthcare environment, discussing system modeling techniques, applications, and research challenges. Various system modeling approaches, including analytical models, Petri nets, and Markov chains, are analyzed to optimize performance, resource allocation, and service quality. Applications of smart healthcare, which include remote monitoring, predictive analytics, and AI-driven healthcare solutions, are discussed in this chapter. After all the significant steps have been taken, existing problems in data security, interoperability, and resource management still remain to be addressed. This chapter concludes by revealing some future research directions: the role of big data analytics, Tactile Internet, and the Internet of Nano Things in forming next-generation smart healthcare systems. The seamless integration of IoT, FC, and CC promises to enhance healthcare efficiency, reduce costs, and improve patient outcomes, driving innovation in the digital health ecosystem.