基于密度泛函理论的第一性原理方法已经成为人们研究材料结构、性质以及进行新功能材 料设计的重要手段。对于掺杂和界面体系，人们常常需要使用超胞来描述。超胞的使用导致能带 折叠，从而掩盖能带结构的重要特征，为人们分析掺杂和界面效应对材料能带结构的影响带来困 难。本文概述了超胞导致的能带折叠现象，重点介绍了基于平面波和原子轨道的能带反折叠方法、 声子能带反折叠方法及相关计算工具，给出了该方法在掺杂和界面体系电子、声子能带结构方面 应用的例子，并对该方法进行了展望。

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.