Predicting new materials through virtually screening a large number of hypothetical materials using supercomputers has enabled materials discovery at an accelerated pace. However, the innumerable number of possible hypothetical materials necessitates the development of faster computational methods for speedier screening of materials reducing the time of discovery. In this thesis, I aim to understand and apply two computational methods for materials prediction. The first method deals with a computational high-throughput study of superalloys. Superalloys are materials which exhibit high-temperature strength. A combinatorial high-throughput search across 2224 ternary alloy systems revealed 102 potential superalloys of which 37 are brand new, all of which we patented. The second computational method deals with a machine-learning (ML) approach and aims at understanding the consistency among five different state-of-the-art machine-learning models in predicting the formation enthalpy of 10 different binary alloys. The study revealed that although the five different ML models approach the problem uniquely, their predictions are consistent with each other and that they are all capable of predicting multiple materials simultaneously.My contribution to both the projects included conceiving the idea, performing calculations, interpreting the results, and writing significant portions of the two journal articles published related to each project. A follow-up work of both computational approaches, their impact, and future outlook of materials prediction are also presented.