First-principles-based multiscale models are ever more successful in addressing the wide range of length and time scales over which material–function relationships evolve in heterogeneous catalysis. They provide invaluable mechanistic insight and allow screening of vast materials spaces for promising new catalysts — in silico and at predictive quality. Here, we briefly review methodological cornerstones of existing approaches and highlight successes and ongoing developments. The biggest challenge is to overcome presently largely static couplings between the descriptions at the various scales to adequately treat the dynamic and adaptive nature of working catalysts. On the road towards a higher structural, mechanistic and environmental complexity, it is, in particular, the fusion with machine learning methodology that promises rapid advances in the years to come. First-principles-based multiscale models provide mechanistic insight and allow screening of large materials spaces to find promising new catalysts. In this Review, Reuter and co-workers discuss methodological cornerstones of existing approaches and highlight successes and ongoing developments in the field.