Noncovalent Interactions in Crystals (P. Gilli and G. Gilli); in: Supramolecular Chemistry: from Molecules to Nanomaterials (J.W. Steed and P.A. Gale eds.) - Volume 6: Supramolecular Materials Chemistry ABSTRACT: The over 500 000 structures collected in current crystallographic databases represent the greatest archive of noncovalent molecular interactions ever conceived by man. Their analysis provides an invaluable basis for understanding these interactions in the crystalline state and for transferring this knowledge to gas phase and condensed phases, such as pure liquids or solutions in polar and nonpolar solvents. This chapter is intended to review the different classes of noncovalent interactions and to supply the mathematical background for their description. For the sake of clarity, the treatment distinguishes between physical and chemical interactions. Physical interactions are considered essentially independent of molecular constitution and deriving from (i) van der Waals forces (atomic repulsion/exchange and attraction/dispersion terms); (ii) electrostatic multipolar forces (mostly monopolar and dipolar terms); and (iii) hydrophobic forces, a kind of interaction that develops in crystal clathrates and water solutions. Conversely, interactions of chemical nature are strictly related to the physicochemical properties of molecules with particular concern for (iv) groups that are either Bronsted acids (proton donors, D–H) or Bronsted bases (proton acceptors, :A) and may interact by forming D–H· · ·:A hydrogen bonds and (v) groups that are either Lewis bases (electron donors, D:) or Lewis acids (electron acceptors, :A) and may interact by forming D:-->A electron donor–acceptor (EDA) or charge-transfer (CT) interactions. Special emphasis is given to interactions that play a determinant structure-directing role in molecular interaction and recognition phenomena, such as hydrogen and halogen bonding. INDEX: 1 Introduction; 1.1 The birth of structural chemistry; 2 A Chemical Classification of Crystals; 2.1 Chemical forces in crystals; 2.2 Metallic crystals; 2.3 Covalent crystals; 2.4 Ionic crystals; 2.5 Molecular crystals; 3 Nonbonded Forces in Molecular Crystals. A Classification; 4 Mostly Physical Intermolecular Forces in Crystals; 4.1 vdW nonbonded forces; 4.2 Electrostatic multipolar forces; 4.3 Hydrophobic forces; 5 Mostly Chemical Intermolecular Forces in Crystals; 5.1 Charge-transfer (CT) or electron donor–acceptor (EDA) interactions; 5.2 Hydrogen bond (H-bond); 6 Conclusions; References