Extreme weather and climate conditions remain a threat to everyday human life. Understanding the atmospheric processes leading to extreme conditions with devastating effects on human lives have become top priority for climate scientists and weather forecasters. Scientists and forecasters require the right tools to be able to reliably forecast and predict the extreme weather and climate events. The challenge in this endeavour lies in the fact that the evolution and movement in space of the atmospheric processes leading to these conditions need to be understood more within a short time scale of a few hours and at local and regional scales of about 1km. This publication explores the potential of advanced numerical methods applied in state-of-the-art NWP and Climate models in improving weather forecasting and climate prediction.