AI methods are rapidly taking hold in almost any aspect of our lives. In some specialized application areas, computers are outperforming humans with respect to image or audio analysis, speech recognition, and controlled movements. Nevertheless, weather and climate prediction still uses humongous computer codes, which solve thousands of differential equations on the fastest supercomputers. Everywhere along the workflow of such prediction systems researchers are trying out how AI could transform or even revolutionize weather and climate forecasting. While there are some promising research pathways, several scientific and technical challenges have to be overcome before we might see a widespread adaptation of such methods in weather centres and research organisations. I will discuss recent achievements and ongoing activities and I may be tempted to speculate about fundamental, inherent limitations of AI concepts in this application area.