Abstract: Large language models have achieved substantial empirical success, but their capability boundaries, applicable scope, and failure mechanisms still lack sufficient theoretical explanation. This article reviews the theoretical limitations of the current large language models paradigm from three perspectives: computational complexity theory, information and coding theory, and statistical learning theory. From the computational perspective, Transformer-based language models can be viewed as computational circuits whose expressiveness is constrained by circuit depth, precision, context length, and generation steps. From the information-theoretic perspective, pretraining can be interpreted as learning a compressor of world corpora, whose capacity is limited by compressibility, Kolmogorov complexity, and scaling-law constraints. From the statistical perspective, next-token prediction forms a high-dimensional learning problem that involves tradeoffs among generalization, memorization, calibration, and hallucination. These analyses suggest that improving model capability should not rely only on scale, but should also consider architecture, data distribution, verification mechanisms, and system-level constraints.