From Passive Metric to Active Signal: The Evolving Role of Uncertainty Quantification in Large Language Models

While Large Language Models (LLMs) show remarkable capabilities, their unreliability remains a critical barrier to deployment in high-stakes domains. This survey charts a functional evolution in addressing this challenge: the evolution of uncertainty from a passive diagnostic metric to an active control signal guiding real-time model behavior. We demonstrate how uncertainty is leveraged as an active control signal across three frontiers: in $\mathbf{\text{advanced}}\mathbf{\text{reasoning}}$ to optimize computation and trigger self-correction; in $\mathbf{\text{autonomous}}\mathbf{\text{agents}}$ to govern metacognitive decisions about tool use and information seeking; and in $\mathbf{\text{reinforcement}}\mathbf{\text{learning}}$ to mitigate reward hacking and enable self-improvement via intrinsic rewards. By grounding these advancements in emerging theoretical frameworks like Bayesian methods and Conformal Prediction, we provide a unified perspective on this transformative trend. This survey provides a comprehensive overview, critical analysis, and practical design patterns, arguing that mastering the new trend of uncertainty is essential for building the next generation of scalable, reliable, and trustworthy AI.