This chapter addresses the theoretical limits and assumptions of large language models not as indicators of system failure but as characteristics that define appropriate usage boundaries. The meaning of benchmark scores depends on which assumptions are in play; limit analysis makes this assumption set visible and thus clarifies in which contexts the model can be positioned as a decision or knowledge source. The probabilistic representation of language, finite context window, and token-level training objective form the computational and representational assumptions; generalization is tied to training–evaluation distributions and task format. The epistemic reliability of the output is context-dependent: where deployment conditions and verification practices align with the model's design assumptions, the output can serve as a knowledge source; outside those conditions, reliability must be secured at the system level, and uncertainty is managed accordingly. Hallucination is framed as a design property that motivates where retrieval, verification modules, or human-in-the-loop should constrain use. Explainability and agent architectures raise the question of how limits are to be managed in practice and which architectural safeguards to deploy. The chapter concludes by emphasising that LLM effectiveness is context-dependent and can be enhanced through retrieval mechanisms, human oversight, and modular verification layers.