In solid-state physics, the electronic band structure (or simply band structure) of a solid describes those ranges of energy, called energy bands, that an electron within the solid may have ("allowed bands"), and ranges of energy called band gaps ("forbidden bands"), which it may not have. Band theory models the behavior of electrons in solids by postulating the existence of energy bands. It successfully uses a material's band structure to explain many physical properties of solids, such as electrical resistivity and optical absorption. Bands may also be viewed as the large-scale limit of molecular orbital theory. A solid creates a large number of closely spaced molecular orbitals, which appear as a band. Band structure derives from the dynamical theory of diffraction of the quantum mechanical electron waves in a periodic crystal lattice with a specific crystal system and Bravais lattice.

The electrons of a single isolated atom occupy atomic orbitals, which form a discrete set of energy levels. If several atoms are brought together into a molecule, their atomic orbitals split, as in a coupled oscillation. This produces a number of molecular orbitals proportional to the number of atoms. When a large number of atoms (of order ×10²⁰ or more) are brought together to form a solid, the number of orbitals becomes exceedingly large. Consequently, the difference in energy between them becomes very small. Thus, in solids the levels form continuous bands of energy rather than the discrete energy levels of the atoms in isolation. However, some intervals of energy contain no orbitals, no matter how many atoms are aggregated, forming band gaps.