Today, patients are demanding a newer and more sophisticated healthcare system, one that is more personalized and matches the speed of modern life. For the latency and energy efficiency requirements to be met for a real-time collection and analysis of health data, an edge computing environment is the answer, combined with 5G speeds and modern computing techniques. Previous healthcare surveys have focused on new fog architecture and sensor types, which leaves untouched the aspect of optimal computing techniques, such as encryption, authentication, and classification that are used on the devices deployed in an edge computing architecture. This paper aims first to survey the current and emerging edge computing architectures and techniques for healthcare applications, as well as identify requirements and challenges of devices for various use cases. Edge computing applications primarily focus on the classification of health data involving vital sign monitoring and fall detection. Other low latency applications perform specific symptom monitoring for diseases, such as gait abnormalities in Parkinson's disease patients. We also present our exhaustive review on edge computing data operations that include transmission, encryption, authentication, classification, reduction and prediction. Even with these advantages, edge computing has some associated challenges, including requirements for sophisticated privacy and data reduction methods to allow comparable performance to their Cloud based counterparts, but with lower computational complexity. Future research directions in edge computing for healthcare have been identified to offer a higher quality of life for users if addressed.