This thesis investigates fundamental and practical aspects of modern quantum information science (QIS) through the lens of Pauli channels — a simple yet powerful class of quantum processes. Three interconnecting themes will be touched on: quantum advantages, quantum noise characterization, and quantum error mitigation: (1) We introduce a novel type of quantum advantages in Pauli channel learning. We show that entanglement with ancillary quantum memory provides exponential advantages in sample complexity for learning a Pauli channel, compared with any entanglement-free learning schemes. These results provide new insight into the role of entanglement as a quantum resource. (2) We advance the understanding of quantum noise by developing a comprehensive theory of learnability in Pauli noise models. Building on techniques from gate-set tomography and algebraic graph theory, we identify which noise parameters can be reliably estimated in the presence of state preparation and measurement (SPAM) errors. We also design efficient, locality-aware protocols for self-consistent learning of Pauli noise, validated experimentally on superconducting qubit platforms. Furthermore, we show how quantum learning advantages can be applied to accelerate noise characterization, even in the presence of imperfect quantum memory. (3) We resolve a critical challenge in Pauli-based quantum error mitigation: the issue of non-identifiability. By leveraging our learnability framework, we propose a gauge-consistent mitigation protocol that remains accurate without relying on unjustified assumptions. The method is scalable and experimentally demonstrates improved performance in regimes where standard approaches fail. Altogether, this thesis offers a unique perspective of the opportunities, challenges, and methodologies of modern QIS, and establishes Pauli channels as a theoretically interesting and practically impactful objects in the research of QIS.