Public emergencies about hygiene and society safety have been the major subjects in current public crisis management. Most of those emergencies exhibit a spatiotemporally evolutional feature. At the same time, Web has been the main source to publish and distribute information about such evolutional emergencies. Therefore, it has been a hot topic in public crisis management and emergency decision to automatically detect evolutional emergencies from the Web and provide early-warning in their early stages. This paper presents the definition of evolutional emergency, which is based on a spatiotemporal viewpoint. We analyze the state-of-the-arts of current research on the detection and early-warning of evolutional public emergencies, and explore the modeling issue of evolutional public emergencies. Then, a research framework for the detection and early-warning of evolutional public emergencies in the Web environment is proposed, which is expected to provide some new prospective for the study on public crisis management and emergency decision in the Web and information era.