Focusing on the atomistic approach to the general equation for the nonequilibrium reversible-irreversible coupling (GENERIC) framework of nonequilibrium thermodynamics, we first summarize the atomistic expressions for the inputs of this framework as previously derived by standard projection-operator methods. We then review to what extent GENERIC can be derived from atomistic principles. In the context of hydrodynamics, we illustrate how one can actually evaluate the atomistic expressions. This example shows what steps are involved in such calculations, and in which direction the formalism needs to be generalized in order to obtain a powerful tool for atomistic calculations for nonequilibrium systems of practical importance.