Heterogeneous catalysis is crucial in many areas of the chemical and energy industries, which was estimated to be used in 90% of all chemical processes despite its importance, most catalysts were found using trial-and-error approaches. Methods that can design new catalysts rationally is highly necessary. One promising approach is to take the advantage of the increasing computational capacity and the state-of-the-art calculation method to screen and design new heterogeneous catalysts. Such an approach requires not only a deep understanding of reaction mechanisms and activities in heterogeneous catalysis, but also rational design schemes. Therefore, in the first half part of the thesis, first-principle calculations within the Density Functional Theory (DFT) framework together with micro-kinetic modelling were used to understand the mechanisms and activities in heterogeneous catalysis. In the second half, some design schemes were proposed including the multi-phase surface design, gradient based optimization and inverse design using activity contribution equation.