Lithography is the process that transfers the structure pattern of integrated circuit device from the mask to the wafer or the surface of other semiconductor substrate, and it is the key technology to implement the mass production of high-end chips. Driven by the Moore’s law, lithography technique has stepped over multiple process nodes from 90 nm to 7 nm and beyond, gradually approaching the physical limit of its resolution. Meanwhile, the lithography image precision is seriously influenced by the diffraction limit property of lithography system, and various system aberrations, errors, and process variations. In this case, the computational lithography techniques must be used to improve the lithography image resolution and fidelity. Computational lithography is a cross research field that involves multiple professional domains, including the optics, semiconductor technology, computing science, image and signal processing, materials science, information science and so on. It is based on the optical imaging and process models, and uses the mathematical methods to simulate and optimize the entire lithography imaging chain, thus realizes the high-precise compensation of the image errors, and is capable of effectively improving the process window and chip manufacturing yield, as well as reducing the research and development cycle and cost of lithography process. To date, it has become one of the core links of the high-end chip manufacturing process. This article first briefly introduces the predecessor of computational lithography, i.e., the traditional resolution enhancement technique, based on which the basic principles, models, and algorithms of computational lithography are introduced. Subsequently, three commonly used computational lithography techniques, including the optical proximity correction, source optimization, and source mask optimization, are reviewed, and the relevant research progress, achievements, and applications are summarized. Finally, this article expounds the current demands and challenges faced by the computational lithography, and discusses the latest technology progress and the future development directions.