In the era when the market segment of Internet of Things (IoT) tops the chart in various business reports, it is apparently envisioned that the field of medicine expects to gain a large benefit from the explosion of wearables and internet-connected sensors that surround us to acquire and communicate unprecedented data on symptoms, medication, food intake, and daily-life activities impacting one's health and wellness. However, IoT-driven healthcare would have to overcome many barriers, such as: 1) There is an increasing demand for data storage on cloud servers where the analysis of the medical big data becomes increasingly complex, 2) The data, when communicated, are vulnerable to security and privacy issues, 3) The communication of the continuously collected data is not only costly but also energy hungry, 4) Operating and maintaining the sensors directly from the cloud servers are non-trial tasks. This book chapter defined Fog Computing in the context of medical IoT. Conceptually, Fog Computing is a service-oriented intermediate layer in IoT, providing the interfaces between the sensors and cloud servers for facilitating connectivity, data transfer, and queryable local database. The centerpiece of Fog computing is a low-power, intelligent, wireless, embedded computing node that carries out signal conditioning and data analytics on raw data collected from wearables or other medical sensors and offers efficient means to serve telehealth interventions. We implemented and tested an fog computing system using the Intel Edison and Raspberry Pi that allows acquisition, computing, storage and communication of the various medical data such as pathological speech data of individuals with speech disorders, Phonocardiogram (PCG) signal for heart rate estimation, and Electrocardiogram (ECG)-based Q, R, S detection.