The increasing volume and sophistication of astrophysical and cosmological data challenge traditional analysis methods, which often struggle with high-dimensional models and complex observations as seen for instance in gravitational waves, supernova cosmology, and gamma-ray data. Highlighting these limitations, this talk explores how deep learning and simulation-based inference can offer scalable and effective solutions. Despite promising advances, there are substantial challenges to fully realize the potential of these technologies. This talk will conclude with the crucial next steps in incorporating these techniques more effectively into astrophysical and cosmological data analysis.