The notions of ionicity and covalency of chemical bonds, effective atomic charges, and decomposition of the cohesive energy into ionic and covalent terms are fundamental yet elusive. For example, different approaches give different values of atomic charges. Pursuing the goal of formulating a universal approach based on firm physical grounds (first-principles or non-empirical), we develop a formalism based on Wannier functions with atomic orbital symmetry and capable of defining these notions and giving numerically robust results that are in excellent agreement with traditional chemical thinking. Unexpectedly, in diamond-like boron phosphide (BP), we find charges of +0.68 on phosphorus and −0.68 on boron atoms, and this anomaly is explained by the Zintl–Klemm nature of this compound. We present a simple model that includes energies of the highest occupied cationic and lowest unoccupied anionic atomic orbitals, coordination numbers, and strength of interatomic orbital overlap. This model captures the essential physics of bonding and accurately reproduces all our results, including anomalous BP.