This book offers a unique and timely contribution to the intersection of agentic AI, reliability engineering, and system trustworthiness. This book addresses both sides of the reliability challenge: how to ensure the reliability of agentic AI systems (with autonomy, planning, and goal-directed behavior), and how agentic AI can be used to enhance the reliability of critical infrastructure and industrial systems (e.g., energy, transportation, manufacturing). It introduces a layered architectural framework that connects technical design (models, execution, cognition) with system-level trust and explainability. This book outlines how awareness and transparency can be engineered into each layer, supporting dependable human-AI collaboration. Beyond technical detail, the book helps researchers, practitioners, and policymakers understand both the barriers and enabling factors for adopting agentic AI in real-world reliability-critical domains. It draws on examples from sectors like power systems, autonomous transportation, and predictive maintenance. This book includes a survey and critical analysis of the current state of regulatory frameworks and standards organizations (e.g., IEEE, ISO, EU AI Act), highlighting gaps and aligning recommendations with the evolving compliance landscape. This book provides an interdisciplinary bridge between AI development, systems reliability engineering, and AI policy/ethics communities—making it relevant for a wide audience across academia, industry, and regulatory bodies.