Heterogeneous catalysis is immensely important to modern and future society. It forms the foundation of chemical industry, supplying essential chemicals and commodities for transport, food production, and pharmaceuticals, and is also a cornerstone in current and future energy platforms. If the long-standing dream of an environmentally sustainable energy sector is to be fulfilled, heterogeneous catalysts aiding production, storage, and use of energy from sustainable sources, e.g. sunlight, wind, and biomass, are expected to be essential. New catalysts improving the efficiency of existing chemical processes, such as ammonia synthesis and sulphur removal in refining, may also contribute to improving future society at large. However, developing the catalysts of tomorrow presents a wealth of scientific challenges. Understanding surface science has always been essential for development and improvement of industrial chemical processes, nano-science and nano-technology, in general any process where a solid surface interacts with any surrounding liquid or gas-phase species. Computational approaches play an increasingly important role in modern surface science, and density functional theory (DFT) in particular. Indeed, several recent developments in our understanding of important aspects of heterogeneous catalysis derive from electronic structure calculations based on DFT. However, there are still many challenges and lots of scope for improvement in the density functional approach to surface science. To mention a few, to improve the accuracy of electronic structure calculations, accuracy of the physical model, completeness of kinetic models for chemical reactions, figuring out the exact state of catalysts under reaction conditions, and also reducing the complexity of our physical models. In this thesis I have analyzed these challenges systematically and have developed some new methods and models to counter those challenges and obtain some general understanding of the catalytic process. I have developed an adsorbate-adsorbate interaction model to include the coverage dependency of the adsorption energy in kinetic models to obtain more accurate catalytic rates than with the commonly used non-interacting mean field model. I then applied the proposed adsorbate-adsorbate interaction model to three important catalytic reactions, the direct NO decomposition, CO methanation, and steam reforming of methane, and analyzed the effect of adsorbate-adsorbate interactions on their catalytic rates. An alloy screening method has also been developed to screen for the industrially most promising alloy catalysts for any catalytic reaction. I have also studied the structure sensitivity of the rates of catalytic direct NO decomposition on different low-index metal surfaces. Furthermore, I have used DFT calculated adsorption and transition state energies coupled with a microkinetic model to study two industrially important catalytic reactions, NH3 oxidation and selective catalytic reduction of NOx, to obtain the catalytic trends and understand the reaction mechanisms.