Artificial intelligence (AI) and machine learning (ML) have recently been radically improved and are now being employed in almost every application domain to develop automated or semi-automated systems. To facilitate greater human acceptability of these systems, explainable artificial intelligence (XAI) has experienced significant growth over the last couple of years with the development of highly accurate models but with a paucity of explainability and interpretability. The literature shows evidence from numerous studies on the philosophy and methodologies of XAI. Nonetheless, there is an evident scarcity of secondary studies in connection with the application domains and tasks, let alone review studies following prescribed guidelines, that can enable researchers’ understanding of the current trends in XAI, which could lead to future research for domain- and application-specific method development. Therefore, this paper presents a systematic literature review (SLR) on the recent developments of XAI methods and evaluation metrics concerning different application domains and tasks. This study considers 137 articles published in recent years and identified through the prominent bibliographic databases. This systematic synthesis of research articles resulted in several analytical findings: XAI methods are mostly developed for safety-critical domains worldwide, deep learning and ensemble models are being exploited more than other types of AI/ML models, visual explanations are more acceptable to end-users and robust evaluation metrics are being developed to assess the quality of explanations. Research studies have been performed on the addition of explanations to widely used AI/ML models for expert users. However, more attention is required to generate explanations for general users from sensitive domains such as finance and the judicial system.