Explainable Artificial Intelligence (XAI) has emerged as a crucial area of research, addressing the opaque nature of deep learning models, which is particularly problematic in high-stakes fields that necessitate interpretability and trust, such as healthcare, finance, and autonomous systems. This review delineates the progression of XAI, with an emphasis on recent advancements, as well as the distinctions between model-specific and model-agnostic methodologies, while critically examining the challenges inherent in reconciling accuracy with transparency. Prominent XAI techniques are systematically discussed, encompassing feature attribution, visual explanations, and both local and global interpretability strategies. A comparative analysis of the applicability and limitations of these techniques within deep learning architectures is provided. Moreover, this paper evaluates training strategies and architectural modifications that are intended to enhance interpretability in neural networks without compromising their performance metrics. A thorough overview of contemporary applications illustrates the integral function of XAI in promoting ethical AI practices and ensuring compliance with regulatory standards. Ultimately, this review aspires to inform future research initiatives by highlighting promising avenues for the development of AI systems that are not only interpretable and robust but also socially responsible.