Industry 4.0 is the latest technological age, in which recent technological developments are being integrated within industrial systems. Consequently, maintenance management of current industrial manufacturing systems is affected by the emergence of the technologies and features of Industry 4.0. This study aimed to conduct a comprehensive literature review to understand how Industry 4.0 technologies and features affect the various functions of maintenance management systems. The reviewing process was initiated by examining the most recent related literature in three different databases. In total, 54 articles were classified into three research categories. Then, the integration of the main functions and components of the adopted maintenance management model and the Industry 4.0 features and technologies were aligned, focusing on the driving force of predictive maintenance. The analysis focused mainly on the technical aspects of the integration process, including integration concepts and integration-assisting tools, identifying the main applications and highlighting the challenges identified in the analysed literature. The key findings were that the main functions of maintenance management systems are significantly influenced by different Industry 4.0 technologies, mainly artificial intelligence–machine learning, CPS, IoT, big data, augmented reality, and cloud computing, in terms of successful integration. Consequently, the overall system implied tangible improvements through the involvement of different Industry 4.0 features which promote real-time condition monitoring, enable data management and curation, increase coordination between various maintenance tasks, facilitate supervision through remote maintenance applications, and, overall, improve operations and productivity, reduce unplanned shutdowns and, as a result, reduce the associated costs. To provide research directions, examples, and methodologies for integrating the various maintenance management system functions with the cutting-edge Industry 4.0 technologies and features based on real and practical cases present in the reviewed literature, the review’s findings are comprehensively categorised and summarised.