Uncertainty quantification (UQ) for large language models (LLMs) is a key building block for safety guardrails of daily LLM applications. Yet, even as LLM agents are increasingly deployed in highly complex tasks, most UQ research still centers on single-turn question-answering. We argue that UQ research must shift to realistic settings with interactive agents, and that a new principled framework for agent UQ is needed. This paper presents three pillars to build a solid ground for future agent UQ research: (1. Foundations) We present the first general formulation of agent UQ that subsumes broad classes of existing UQ setups; (2. Challenges) We identify four technical challenges specifically tied to agentic setups -- selection of uncertainty estimator, uncertainty of heterogeneous entities, modeling uncertainty dynamics in interactive systems, and lack of fine-grained benchmarks -- with numerical analysis on a real-world agent benchmark, $τ^2$-bench; (3. Future Directions) We conclude with noting on the practical implications of agent UQ and remaining open problems as forward-looking discussion for future explorations.