Computational imaging describes the whole imaging process from the perspective of light transport and information transmission, features traditional optical computing capabilities, and assists in breaking through the limitations of visual information recording. Progress in computational imaging promotes the development of diverse basic and applied disciplines. In this review, we provide an overview of the fundamental principles and methods in computational imaging, the history of this field, and the important roles that it plays in the development of science. We review the most recent and promising advances in computational imaging, from the perspective of different dimensions of visual signals, including spatial dimension, temporal dimension, angular dimension, spectral dimension, and phase. We also discuss some topics worth studying for future developments in computational imaging.