The semiconductor industry enabling numerous electronic devices that empower the digital era has arrived at a turning point in recent years. Traditional silicon (Si)-based devices are about to reach the material limit as a result of extreme scaling of gate length below 10nm, leading to the forthcoming end of Moore's law. One of the proposed ways to advance beyond Moore's law is to use alternative, advanced semiconducting materials such as indium gallium arsenide (InGaAs) and gallium oxide (Ga2O3), mainly for their superior electronic properties compared to traditional semiconductors. However, a series of major challenges need to be overcome in order for these materials to live up to their promise, including insufficiently high dopant activation and insufficiently low contact resistivity for InGaAs, and strong degree of dopant segregation towards the surface for Ga2O3. In this thesis, we address these challenges with a computational modeling approach, based on ab initio density functional theory calculations. Our main findings include: (1) formation and binding of negatively-charged cation vacancies are the major contributor of charge compensation in heavily Si-doped InGaAs; (2) composition, surface termination, doping concentration, compositional grading and metal-semiconductor alloying can all affect the contact resistivity of InGaAs; (3) in random InGaAs, vibrational modes associated with shallow n-type dopants (Si, Se) and defects (cation vacancies) assume band-like distribution with many satellite peaks, in contrast with the single-peak signature of the same impurities in binary compounds (GaAs, InAs); and (4) Sn has the strongest tendency to segregate towards the (010) surface of Ga2O3 among three common shallow n-type dopants (Si, Ge, Sn), and the presence of negatively-charged surface Ga vacancies drastically enhance the segregation effect due to Coulomb interaction. This work would serve as a guidance for further experimentation and engineering with advanced semiconducting materials in electronic device applications.