This PhD dissertation investigates the phenomenon of extreme outflows in quasars and its implications for galaxy evolution and quasar feedback. The study focuses on two distinct quasar populations: extremely red quasars (ERQs) and normal quasars, both exhibiting powerful outflows, but in different contexts. The first part of the dissertation explores a population of extremely red quasars (ERQs) with exceptionally fast outflows, likely representing a young stage of galaxy evolution. The ERQs, situated at a median redshift of ? ≈ 2.6, are studied through Keck/KCWI integral field spectra of 11 quasars. Analysis of their properties, such as median color (?–?3 = 5.9 mag), median bolometric luminosity (⟨?bol⟩ ≈ 5 × 10^47 erg/s), Ly? halo luminosity (⟨?halo⟩ = 5 × 10^43 erg/s), and maximum linear size (>128 kpc), reveals similarities to blue quasars while exhibiting unique characteristics. The ERQ halos have compact and circularly symmetric inner regions, and they are kinematically quiet. Despite their powerful outflows, there is no clear evidence for feedback on circumgalactic scales, potentially due to long outflow travel times. The dissertation also confirms the importance of narrow Ly? emission spikes in ERQ aperture spectra for systemic redshift determination and measuring outflow speeds. In the second part, the dissertation investigates the driving factors behind fast outflows in normal quasars using a large sample of 39,249 quasars at a median redshift of ⟨?⟩ ≈ 2.17. Redshifts based on the Mg ii emission line are re-measured, enabling the exploration of unprecedented outflow velocities (>6000 km s−1) while ensuring statistical significance and uniformity. Analysis reveals significant correlations, indicating that higher Eddington ratios and softer far-UV continua (h? >54.4 eV) are primary contributors to faster outflows. Supporting evidence suggests that radiative line-driving may generate extreme outflow velocities, influenced by multiple factors. This study emphasizes the importance of considering a multi-dimensional parameter space to understand the fundamental causes of extreme outflows in quasars. In conclusion, this comprehensive dissertation provides valuable insights into extreme outflows in quasars, encompassing both ERQs and normal quasars. The findings contribute to our understanding of the early stages of galaxy evolution and the impact of quasar feedback on host galaxies. The study highlights the complexities of quasar outflows and their driving mechanisms, underscoring the significance of multi-dimensional analyses in future studies.