In recent years, the manufacturing sector has seen an influx of artificial intelligence applications, seeking to harness its capabilities to improve productivity. However, manufacturing organizations have limited understanding of risks that are posed by the usage of artificial intelligence, especially those related to trust, responsibility, and ethics. While significant effort has been put into developing various general frameworks and definitions to capture these risks, manufacturing and supply chain practitioners face difficulties in implementing these and understanding their impact. These issues can have a significant effect on manufacturing companies, not only at an organization level but also on their employees, clients, and suppliers. This paper aims to increase understanding of trustworthy, responsible, and ethical Artificial Intelligence challenges as they apply to manufacturing and supply chains. We first conduct a systematic mapping study on concepts relevant to trust, responsibility and ethics and their interrelationships. We then use a broadened view of a machine learning lifecycle as a basis to understand how risks and challenges related to these concepts emanate from each phase in the lifecycle. We follow a case study driven approach, providing several illustrative examples that focus on how these challenges manifest themselves in actual manufacturing practice. Finally, we propose a series of research questions as a roadmap for future research in trustworthy, responsible and ethical artificial intelligence applications in manufacturing, to ensure that the envisioned economic and societal benefits are delivered safely and responsibly.