Smart healthcare systems require recording, transmitting and processing large volumes of multimodal medical data generated from different types of sensors and medical devices, which is challenging and may turn some of the remote health monitoring applications impractical. Moving computational intelligence to the network edge is a promising approach for providing efficient and convenient ways for continuous-remote monitoring. Implementing efficient edge-based classification and data reduction techniques are of paramount importance to enable smart healthcare systems with efficient real-time and cost-effective remote monitoring. Thus, we present our vision of leveraging edge computing to monitor, process, and make autonomous decisions for smart health applications. In particular, we present and implement an accurate and lightweight classification mechanism that, leveraging some time-domain features extracted from the vital signs, allows for a reliable seizures detection at the network edge with precise classification accuracy and low computational requirement. We then propose and implement a selective data transfer scheme, which opts for the most convenient way for data transmission depending on the detected patient’s conditions. In addition to that, we propose a reliable energy-efficient emergency notification system for epileptic seizure detection, based on conceptual learning and fuzzy classification. Our experimental results assess the performance of the proposed system in terms of data reduction, classification accuracy, battery lifetime, and transmission delay. We show the effectiveness of our system and its ability to outperform conventional remote monitoring systems that ignore data processing at the edge by: (i) achieving 98.3% classification accuracy for seizures detection, (ii) extending battery lifetime by 60%, and (iii) decreasing average transmission delay by 90%.