This paper undertakes a systematic review of relevant extant literature to consider the potential societal implications of the growth of AI in manufacturing. We analyze the extensive range of AI applications in this domain, such as interfirm logistics coordination, firm procurement management, predictive maintenance, and shop-floor monitoring and control of processes, machinery, and workers. Additionally, we explore the uncertain societal implications of industrial AI, including its impact on the workforce, job upskilling and deskilling, cybersecurity vulnerability, and environmental consequences. After building a typology of AI applications in manufacturing, we highlight the diverse possibilities for AI's implementation at different scales and application types. We discuss the importance of considering AI's implications both for individual firms and for society at large, encompassing economic prosperity, equity, environmental health, and community safety and security. The study finds that there is a predominantly optimistic outlook in prior literature regarding AI's impact on firms, but that there is substantial debate and contention about adverse effects and the nature of AI's societal implications. The paper draws analogies to historical cases and other examples to provide a contextual perspective on potential societal effects of industrial AI. Ultimately, beneficial integration of AI in manufacturing will depend on the choices and priorities of various stakeholders, including firms and their managers and owners, technology developers, civil society organizations, and governments. A broad and balanced awareness of opportunities and risks among stakeholders is vital not only for successful and safe technical implementation but also to construct a socially beneficial and sustainable future for manufacturing in the age of AI.