Solid-state materials with spin defects are emerging platforms for quantum technologies. These optically addressable defects, with unique quantum properties, are poised to drive significant advancements in these fields. Central to understanding and leveraging these properties are first-principles calculations, which enable researchers to identify the atomic structures of point defects and discover novel defects with enhanced performance for quantum applications. This dissertation focuses on the intricate world of spin defects in silicon carbide (SiC), a technologically mature semiconducting material. By harnessing first-principle calculations, we studied various spin defects in bulk and near-surface environments, uncovered their complex behaviors, and contributed to the advancement of quantum technologies.In Chapter 1, we briefly introduce the requirements for the physical implementation of quantum technologies based on solid-state spin defects. Starting with the prototypical nitrogen-vacancy (NV) center in diamond, we discuss the criteria for evaluating and screening novel spin defects. We also present SiC as a material platform and show the general strategy of this dissertation to study the spin defects in SiC with first-principles calculations. In Chapter 2, we provide a general overview of the first-principles methodology used throughout the rest of the chapters. After briefly introducing the Kohn-Sham formulation of density functional theory, we focus on computing the critical properties of spin defects, including formation energy, zero-phonon lines (ZPLs), and spin Hamiltonian parameters.In Chapter 3, we apply first-principles calculations to investigate the physical properties of the negatively charged NV center in 4H-SiC. We show that this defect is sensitive to strain and lattice symmetry. The measured and computed ZPLs are in agreement and consistent for different geometrical configurations. The computed ZPLs are extremely sensitive to the geometrical configurations, and large supercells with more than 2,000 atoms are required to obtain accurate numerical results. We find that the computed decoherence time of the basal NV centers at zero magnetic fields is substantially larger than that of the axial configurations. To further understand the optical manipulation of the spin defects, in Chapter 4, we shift our focus to the photoionization process of the spin defects in SiC. Our theoretical studies can predict the optimal laser energy to be used to manipulate the charge state of the divacancy in this spin-to-charge conversion process, enabling a single-shot readout scheme to be implemented to measure long spin coherence times. As the realization of quantum sensors or spin-photon interfaces requires positioning spin defects near a surface or interface, in Chapter 5, we study the divacancy in 3C-SiC in the proximity of surfaces as a function of different surface reconstructions and terminations. We show that a divacancy close to hydrogen-terminated (2*1) surfaces is a robust spin defect with a triplet ground state and slight variations of many of its physical properties relative to the bulk. However, the Debye-Waller factor decreases in the vicinity of the surface and may be further improved by strain engineering. Our results show that the divacancy close to SiC surfaces is a promising spin defect for quantum applications, similar to its bulk counterpart.