Chemical bonding concepts like covalency, ionicity, Pauli repulsion, shared-electron, or donor-acceptor bonding are important tools to sort our vast knowledge in chemistry and predict new reactivity. Electronic structure analysis provides the basis for a detailed understanding of the origins of these concepts. Energy decomposition analysis (EDA) is an established method for molecules and has recently been implemented for application in extended systems, that is, surfaces and solids, where it is termed periodic EDA (pEDA). The foundations and applications of this method which enables the derivation of bonding concepts are outlined in this review. Embedded in key examples from molecular and solid-state chemistry, the major part covers the adsorption and reactivity of molecules with surfaces with a focus on organic molecules interacting with semiconductor surfaces. Based on electronic structure analysis and supported by a quantitative methodology, we show that analogous bonding concepts can be applied in diverse chemical environments. This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods Structure and Mechanism > Computational Materials Science K E Y W O R D S chemical bonding, density functional theory, energy decomposition analysis, surface chemistry 1 | INTRODUCTIONThe chemical bond is the central concept in the discussion of structures and reactivity in chemistry. The nature of the forces that hold atoms together thrills chemists since the upcoming of atomistic theories. First realistic models were derived more than two centuries ago based on experimental observations. 1 The paradigm shift at the beginning of the 20th century then provided the basis for our present-day understanding of chemical bonding in terms of quantum mechanical principles. 2,3 But by no means did this development end the discussion about chemical bonding and the interpretation of results obtained by theory and computation. The intrinsic ambiguity in discussing often nonobservable properties that are connected to very useful concepts like covalency, ionicity, Pauli repulsion, bond order, and alike fosters the scientific discussion and leads to a further refinement of our understanding of the chemical bond. [4][5][6][7][8][9][10][11] The development of bonding concepts in molecular and solid-state chemistry evolved separately for the most part. For molecules, the view on (more or less) localized bonds as given by the Lewis picture more than a century ago 12 was regained both by valence bond (VB) theory and from the molecular orbital (MO) approach by the linear combination of atomic orbitals (LCAO) and localization procedures. [13][14][15][16] This resulted in the development of many powerful methods for electronic structure analysis for the qualitative and quantitative interpretation of chemical bonding that have been summarized in previous reviews. 2,17-21 Some examples will be discussed in the next section. In the field of surfaces and solids, the delocalized view