Alternative catalysts is based on inexpensive and environmental-friendly metals for propane dehydrogenation (PDH) catalysts are needed to overcome the drawbacks of Pt or Cr-based commercial catalysts. A thorough understanding of current catalysts is required to further optimize or design novel catalysts. As such, this dissertation employs Density Functional Theory (DFT) in tandem with ab initio thermodynamics, grand canonical Monte Carlo (GCMC), and Machine Learning (ML) to understand the mechanisms of catalytic performance and phase formation, which are used to design new catalysts. The DFT calculations, in accordance with ab initio thermodynamics, are used to determine surface stability as a function of reaction environment. It is demonstrated that the carbon-rich surfaces of Fe3C exhibit high stability under typical PDH reaction conditions. Further investigation into kinetics shows that these surfaces are responsible for high selectivity by destabilizing propylene adsorption through the ensemble effect. In particular, this dissertation develops a hybrid grand canonical Monte Carlo-Density Functional Theory (GCMC-DFT) method that can effectively sample the structures in complex phase formation without any prior information or parameters about the system. It is shown that the ring formation and ring completion are essential in coke formation on Fe surfaces. Both electronic and geometrical effect can improve the coke resistance of iron-based catalysts. DFT calculated adsorption energies coupled with machine learning are utilized to effectively search through a certain material space and design new catalysts. A Co3Si material is identified to be active and selective for PDH. Silicon promotes cobalt to be selective by downshifting the d-band and destabilizing propylene adsorption. The multi-scale computational methodology developed and applied in this dissertation can provide deep understanding of Fe-based PDH catalysts and assist in designing new catalysts, and can be readily transferred to other catalytic research works.