Natural disasters and epidemics are unfortunate recurring events that lead to huge societal and economic loss. Recent advances in supercomputing can facilitate simulations of such scenarios in (or even ahead of) real-time, therefore supporting the design of adequate responses by public authorities. By incorporating high-velocity data from sensors and modern high-performance computing systems, ensembles of simulations and advanced analysis enable urgent decision-makers to better monitor the disaster and to employ necessary actions (e.g., to evacuate populated areas) for mitigating these events. Unfortunately, frameworks to support such versatile and complex workflows for urgent decision-making are only rarely available and often lack in functionalities. This paper gives an overview of the VESTEC project and framework, which unifies orchestration, simulation, in-situ data analysis, and visualization of natural disasters that can be driven by external sensor data or interactive intervention by the user. We show how different components interact and work together in VESTEC and describe implementation details. To disseminate our experience three different types of disasters are evaluated: a Wildfire in La Jonquera (Spain), a Mosquito-Borne disease in two regions of Italy, and the magnetic reconnection in the Earth magnetosphere.