Quantum-mechanical and classical embedding schemes both employ effective operators that incorporate the environmental effects for local properties. Despite their common goal, the two methods follow rather different philosophies: quantum-mechanical density-based embedding schemes aim at a reformulation of density-functional theory methods through a subsystem formalism, while in classical polarizable embedding models, perturbation theory is employed to derive and parametrize the effective operators. In this book chapter, we derive these two methodologies in a common framework, highlighting the common ideas as well as differences between them. We further review the latest extensions to these methodologies as well as recent applications to local absorption properties of small molecules as well as the green fluorescent protein.