Every year, natural disasters cause major loss of human life, damage to infrastructure and significant economic impact on the areas involved. Geospatial Scientists aim to help in mitigating or managing such hazards by computational modeling of these complex events, while Information Communication Technology (ICT) supports the execution of various models addressing different aspects of disaster management. The execution of natural hazard models using traditional ICT foundations is not possible in a timely manner due to the complex nature of the models, the need for large-scale computational resources as well as intensive data and concurrent-access requirements. Cloud Computing can address these challenges with near-unlimited capacity for computation, storage, and networking, and the ability, to offer natural hazard modeling systems as end services, has now become more realistic than ever. However, researchers face several open challenges in adopting and utilizing Cloud Computing technologies during disasters. As such, this survey paper aggregates all these challenges, reflects on the current research trends and outlines a conceptual Cloud-based solution framework for more effective natural hazards modeling and management systems using Cloud infrastructure in conjunction with other technologies such as Internet of Things (IoT) networks, fog, and edge computing. We draw a clear picture of the current research state in the area and suggest further research directions for future systems.