The Internet of Things (IoT) has radically changed the industrial world, enabling the integration of numerous systems and devices into the industrial ecosystem. There are many areas of the manufacturing industry in which IoT has contributed, including plants’ remote monitoring and control, energy efficiency, more efficient resources management, and cost reduction, paving the way for smart manufacturing in the framework of Industry 4.0. This review article provides an up-to-date overview of IoT systems and machine learning (ML) algorithms applied to smart manufacturing (SM), analyzing four main application fields: security, predictive maintenance, process control, and additive manufacturing. In addition, the paper presents a descriptive and comparative overview of ML algorithms mainly used in smart manufacturing. Furthermore, for each discussed topic, a deep comparative analysis of the recent IoT solutions reported in the scientific literature is introduced, dwelling on the architectural aspects, sensing solutions, implemented data analysis strategies, communication tools, performance, and other characteristic parameters. This comparison highlights the strengths and weaknesses of each discussed solution. Finally, the presented work outlines the features and functionalities of future IoT-based systems for smart industry applications.