  Language Models (LMs) have demonstrated exceptional performance across
various Natural Language Processing (NLP) tasks. Despite these advancements,
LMs can inherit and amplify societal biases related to sensitive attributes
such as gender and race, limiting their adoption in real-world applications.
Therefore, fairness has been extensively explored in LMs, leading to the
proposal of various fairness notions. However, the lack of clear agreement on
which fairness definition to apply in specific contexts (\textit{e.g.,}
medium-sized LMs versus large-sized LMs) and the complexity of understanding
the distinctions between these definitions can create confusion and impede
further progress. To this end, this paper proposes a systematic survey that
clarifies the definitions of fairness as they apply to LMs. Specifically, we
begin with a brief introduction to LMs and fairness in LMs, followed by a
comprehensive, up-to-date overview of existing fairness notions in LMs and the
introduction of a novel taxonomy that categorizes these concepts based on their
foundational principles and operational distinctions. We further illustrate
each definition through experiments, showcasing their practical implications
and outcomes. Finally, we discuss current research challenges and open
questions, aiming to foster innovative ideas and advance the field. The
implementation and additional resources are publicly available at
https://github.com/LavinWong/Fairness-in-Large-Language-Models/tree/main/definitions.
