Coarse graining is a methodology investigating the mesoscopic range and the importance of atomistic detail across scales. This approach reduces the system complexity by lumping together degrees of freedom into coarse-grained variables. Estimating, equilibrium or non equilibrium, quantities of interest for the atomistic model using the approximating coarse grained model inevitably leads to errors. The use of information-theoretic methods is a rigorous mathematical approach that provide the tools in quantifying such errors and suggesting effective coarse models both for the equilibrium and the dynamics of the system.