Large language models (LLMs) are trained on web-scale corpora that exhibit steep power-law distributions, in which the distribution of knowledge is highly long-tailed, with most appearing infrequently. While scaling has improved average-case performance, persistent failures on low-frequency, domain-specific, cultural, and temporal knowledge remain poorly characterized. This paper develops a structured taxonomy and analysis of long-Tail Knowledge in large language models, synthesizing prior work across technical and sociotechnical perspectives. We introduce a structured analytical framework that synthesizes prior work across four complementary axes: how long-Tail Knowledge is defined, the mechanisms by which it is lost or distorted during training and inference, the technical interventions proposed to mitigate these failures, and the implications of these failures for fairness, accountability, transparency, and user trust. We further examine how existing evaluation practices obscure tail behavior and complicate accountability for rare but consequential failures. The paper concludes by identifying open challenges related to privacy, sustainability, and governance that constrain long-Tail Knowledge representation. Taken together, this paper provides a unifying conceptual framework for understanding how long-Tail Knowledge is defined, lost, evaluated, and manifested in deployed language model systems.