Abstract: First-principles methods based on the density-functional theory have been widely applied to investigate structures and properties of materials and further to design new functional materials. The supercell method is usually used for the modeling of doped systems and interfaces. Unfortunately, the use of supercells leads to band foldings. As a result, the nature of electronic bands may be hidden, which brings difficulties in understanding the effects of doping and interfacing on the band structure of materials. This review provides recent advances in band unfolding technique within the plane-wave method and the linear combination of atomic orbitals. It also gives unfolding of phononic bands and lists a number of codes for band unfolding calculations. Finally, it presents a few applications of the technique and an outlook on further research options.

Key words: first-principles, band unfolding, band structure, doping, interface