State-of-the-art AI-based numerical weather prediction models (AI-NWP) produce forecasts that are comparable or even outperform conventional forecasting systems while being orders of magnitude faster. Since climate projections are obtained by simulating the long-term evolution of weather states with appropriate forcing, the use of AI-NWP models for climate modeling is a promising avenue that has received little attention so far. We present two applications of AI-NWP models for climate modeling: (i) downscaling and (ii) weather forecasting initialised from climate projection data. Both applications use ERA5-pre-trained AI-NWP models without fine-tuning for the tasks or for the input data. For downscaling, we use low-resolution CMIP6 simulation data as initial condition and obtain high-resolution, bias corrected output fields by performing short-term forecasting with the existing model; see Fig. 1 for an example. Our results show a remarkable robustness of AI-NWP to unseen states from historical and climate simulations of different resolutions. For AI-based weather forecasting in future climates, we obtain almost unchanged RMSE scores in a 2o warmer climate although a more detailed analysis shows a cold bias in the forecasts. We believe that differences between climate model results and AI-NWP forecasts have the potential to provide insights into the physics and deficiencies of both climate models (e.g. for short time scales) and AI-NWP models (on long time scales). Based on our results, we discuss how existing AI-NWP models can be extended for climate projections, e.g. to sample extreme weather events, and hence help with adaptation to climate change.