Artificial intelligence models encounter significant challenges due to their black-box nature, particularly in safety-critical domains such as healthcare, finance, and autonomous vehicles. Explainable Artificial Intelligence (XAI) addresses these challenges by providing explanations for how these models make decisions and predictions, ensuring transparency, accountability, and fairness. Existing studies have examined the fundamental concepts of XAI, its general principles, and the scope of XAI techniques. However, there remains a gap in the literature as there are no comprehensive reviews that delve into the detailed mathematical representations, design methodologies of XAI models, and other associated aspects. This paper provides a comprehensive literature review encompassing common terminologies and definitions, the need for XAI, beneficiaries of XAI, a taxonomy of XAI methods, and the application of XAI methods in different application areas. The survey is aimed at XAI researchers, XAI practitioners, AI model developers, and XAI beneficiaries who are interested in enhancing the trustworthiness, transparency, accountability, and fairness of their AI models.