Frames were introduced by Duffin and Schaeffer in 1952 in the context of nonharmonic Fourier series. After a rapid development in the past decade, frame theory has been widely used to develop innovative techniques in tackling many challenging problems in engineering applications including signal analysis and image processing. It also plays a central role in some theoretical developments in other areas of mathematics including wavelet analysis, time-frequency analysis, sampling theory, operator theory and representation theory, nonlinear sparse approximation, pseudo-differential operators, and quantum computation.