Computational thermodynamics, known as CALPHAD method when dawned in 1950s, aimed at coupling phase diagrams with thermochemistry by computational techniques. It eventually evolves toward kinetic simulations integrated with thermodynamic calculations, i.e., computational kinetics, including diffusion-controlled phase transformation, precipitation simulation, and phase-field simulation. In the meantime, thermodynamic, mobility, and physical property databases for multi-component and multi-phase materials, served as basic knowledge for materials design, are critically evaluated by CALPHAD approach combining key experiments, first-principles calculations, statistic methods, and empirical theories. The combination of these computational techniques with their conjugated databases makes it possible to simulate phase transformations and predict the microstructure evolution in real materials in a foreseeable future. Further links to microand macro-scale simulations lead to a multi-scale computational framework, and aid the search for the quantitative relations among chemistry, process, microstructures, and materials properties in order to accelerate materials development and deployment. This is a new route of materials and process design pursued by Integrated Computational Materials Engineering (ICME) and Materials Genome Initiative (MGI). This article presents a review on the basic theories and applications, the state of the art and perspective of computational thermodynamics and kinetics.