Language Models (LMs) have significantly advanced natural language processing and enabled remarkable progress across diverse domains, yet their black-box nature raises critical concerns about the interpretability of their internal mechanisms and decision-making processes. This lack of transparency is particularly problematic for adoption in high-stakes domains, where stakeholders need to understand the rationale behind model outputs to ensure accountability. On the other hand, while explainable artificial intelligence (XAI) methods have been well studied for non-LMs, they face many limitations when applied to LMs due to their complex architectures, considerable training corpora, and broad generalization abilities. Although various surveys have examined XAI in the context of LMs, they often fail to capture the distinct challenges arising from the architectural diversity and evolving capabilities of these models. To bridge this gap, this survey presents a comprehensive review of XAI techniques with a particular emphasis on LMs, organizing them according to their underlying transformer architectures: encoder-only, decoder-only, and encoder-decoder, and analyzing how methods are adapted to each while assessing their respective strengths and limitations. Furthermore, we evaluate these techniques through the dual lenses of plausibility and faithfulness, offering a structured perspective on their effectiveness. Finally, we identify open research challenges and outline promising future directions, aiming to guide ongoing efforts toward the development of robust, transparent, and interpretable XAI methods for LMs.