The testing of the components of global climate models is a paramount step before the performance of coupled systems can be assessed and understood. One such component of an atmospheric model is the dynamical core that describes the resolved fluid flow equations and determines the numerical scheme, the computational grid and its grid staggering options, the diffusion properties and the parallel scaling efficiency. The paper surveys a wide spectrum of idealized dynamical core tests and demonstrate how they reveal the properties of more complex model simulations. They do so at reduced computational cost and serve as a rapid model assessment tool. Dry and idealized-moist test cases are featured, both with and without topography on regular-size and small-size planets. The assessments focus on advection schemes and their subgrid-scale mixing properties, the effective resolution of models, the consistency between the dynamical core and the tracer transport algorithm, baroclinic waves and gravity waves, idealized tropical cyclones, and stratospheric motions, like the tropical Quasi-Biennial Oscillation (QBO) or polar Sudden Stratospheric Warmings, which depend critically on the diffusive properties of the dynamical cores. The paper showcases selected model results which include examples from the DoE-supported Dynamical Core Model Intercomparison Project (DCMIP) in 2012. Special attention is also paid to the impact of model resolution, which incorporates both variable-resolution simulations with the Spectral Element (SE) Community Atmosphere Model (CAM) and the impacts of increased vertical resolutions on the circulation.