A rigorous definition of atomic orbitals that invokes concepts of the quantum-mechanical theory of atoms in molecules is presented. Being free of any references to nuclei-centered basis functions, this new definition is universally applicable to wave functions furnished by all types of electronic structure calculations. The atomic orbitals in molecules (AOIMs) it produces are continuous and orthonormal. In most cases, linear combinations of only a few such AOIMs accurately represent individual molecular orbitals (MOs) and strongly occupied natural orbitals (NOs). The coefficients of these linear combinations are remarkably insensitive to the quality of basis sets used in the generation of the MOs and NOs. These properties make the AOIMs particularly suitable for compact description of bonding in diverse chemical systems.