ClimaCore.jl constitutes the dynamical core (dycore) of the atmosphere and land models for CliMA's Earth System Model (ESM). ClimaCore.jl provides flexible and composable discretization tools to solve the governing equations of the ESM component models. In fact, ClimaCore.jl's high-level application programming interface (API) facilitates modularity and composition of differential operators and the definition of flexible discretizations. This, in turn, is coupled with low-level APIs that support different data layouts, specialized implementations, and flexible models for threading, to better face high-performance optimization, data storage, and scalability challenges on modern HPC architectures.