Diverse edge sensing devices are expected to reach 10-100 per person in the next decade, produce continuous, heterogeneous data at unprecedented volume, and enable numerous novel applications. We propose a new disciplinary concept of computational Screening and Surveillance (CSS) that utilizes edge learning to collect, analyze and interpret both physical and physiologic data of human subjects, to detect early indicators of diseases, and monitor health changes in both individuals and populations. Real-time information, knowledge, and insights from extreme-scale CSS will revolutionize our understanding, prediction, intervention, treatment, and management of acute/infectious (e.g. flu, COVID), chronic physical and psychological/psychiatric diseases, resulting in huge savings for numerous diseases each costing hundreds of billion dollars every year. This proposal will (i) engage diverse academic, health, community, and government stakeholders to collectively define the functional and performance requirements for Computational Screening and Surveillance; (ii) investigate and apply principles of extreme-scale edge learning to research challenges in four areas of algorithms & theory, security & privacy (S&P), systems, and architecture in CSS; and (iii) design, develop systematic solutions, methodologies and tools considering accuracy, correctness, security and privacy, evaluate and validate their performance both experimentally and theoretically for extreme-scale CSS.