This systematic review examines the use of edge artificial intelligence (AI) and wearable sensors for real-time patient monitoring in smart hospitals and home settings, focusing on detecting deterioration, falls, arrhythmias, and infection-related changes. The review synthesizes studies from 2017 to 2026 on edge AI architectures, wearable sensor fusion, and clinical alert systems, emphasizing latency, power constraints, alert performance, and integration into clinical workflows. A PRISMA 2020-compliant search identified 127 studies from 2,100 records, with findings showing that while edge AI execution grew post-2020, it still represented a minority of designs. Sensor fusion was often linked to broader event coverage but increased implementation complexity. The review concludes that edge AI can reduce latency and enhance privacy but introduces challenges related to power usage, model complexity, device reliability, and maintenance, with limited clinical validation of alert systems and few studies addressing alert fatigue or clinician response.