In recent years, numerous explainable artificial intelligence (XAI) use cases have been developed, to solve numerous real problems in industrial applications while maintaining the explainability level of the used artificial intelligence (AI) models to judge their quality and potentially hold the models accountable if they become corrupted. Therefore, understanding the state-of-the-art methods, pointing out recent issues, and deriving future directions are important to drive XAI research efficiently. This paper presents a systematic literature review of local explanation techniques and their practical applications in various industrial sectors. We first establish the need for XAI in response to opaque AI models and survey different local explanation methods for industrial AI applications. The number of studies is then examined with several factors, including industry sectors, AI models, data types, and XAI-based usage and purpose. We also look at the advantages and disadvantages of local explanation methods and how well they work in practical settings. The difficulties of using local explanation techniques are also covered, including computing complexity and the trade-off between precision and interpretability. Our findings demonstrate that local explanation techniques can boost industrial AI models’ transparency and interpretability and give insightful information about them. The efficiency of these procedures must be improved, and ethical concerns about their application must be resolved. This paper contributes to the increasing knowledge of local explanation strategies and offers guidance to academics and industry professionals who want to use these methods in practical settings.