We investigate historical simulations of relevant components of the Arctic energy and water budgets for 39 Coupled Model Intercomparison Project Phase 6 (CMIP6) models and validate them against observation-based estimates. We look at simulated seasonal cycles, long-term averages and trends of lateral transports and storage rates in atmosphere and ocean as well as vertical fluxes at top-of-atmosphere and the surface. We find large inter-model spreads and systematic biases in the representation of annual cycles and long-term averages. Surface freshwater fluxes associated with precipitation and evaporation as well as runoff from Arctic lands tend to be overestimated by most CMIP6 models and about two thirds of the analysed models feature an early timing bias of one month in the runoff cycle phase, related to an early snow melt bias and the lack of realistic river routing schemes. Further, large biases are found for oceanic volume transports, partly because data required for accurate oceanic transport computations has not been archived. Biases are also present in the simulated energy budget components. The net vertical energy flux out of the ocean at the Arctic surface as well as poleward oceanic heat transports are systematically underestimated by all models. We find strong anti-correlation between average oceanic heat transports and mean sea ice cover, atmospheric heat transports, and also the long-term ocean warming rate. The latter strongly suggests that accurate depiction of the mean state is a prerequisite for realistic projections of future warming of the Arctic. Our diagnostics also provide useful process-based metrics for model selection to constrain projections.