Agentic AI systems built on large language models can plan over multiple steps, use external tools, retain information in memory, and coordinate with other agents. These capabilities make them more useful than static language models, but they also introduce new security and operational risks. Untrusted content from websites, emails, documents, and databases can enter the same context as system instructions; persistent memory can carry compromised information across sessions; and access to external tools can turn an incorrect model response into a consequential real-world action. This article reviews the trustworthiness of agentic AI across five interconnected dimensions: safety and robustness, alignment and human oversight, transparency and auditability, privacy and data governance, and regulatory compliance. It organizes key failure modes, including indirect prompt injection, backdoor triggers, goal misgeneralization, memory contamination, and cross-session data leakage, into a unified taxonomy. It also examines major mitigation approaches, such as instruction hierarchies, context isolation, spotlighting, process-based supervision, constrained tool use, and privacy-preserving memory, while distinguishing techniques supported by empirical evidence from those that remain largely conceptual. Building on this analysis, we introduce the Trustworthy Agent Development Lifecycle (TADL), a six-phase framework covering specification, design, training, evaluation, deployment, and monitoring. For each phase, TADL identifies relevant trust activities, expected evidence, and risk-based decision gates. Although TADL has not yet been empirically validated, it provides a structured foundation for developing and evaluating more secure and accountable agentic systems. The article concludes by identifying gaps in current benchmarks and outlining priorities for future research.

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