Purpose - Powder bed fusion additive manufacturing (PBFAM) of metal components has attracted much attention, but the inability to quickly and easily ensure quality has limited its industrial use. Since the technology is currently being investigated for critical engineered components and is largely considered unsuitable for high volume production, traditional statistical quality control methods cannot be readily applied. An alternative strategy for quality control is to monitor the build in real time with a variety of sensing methods and, when possible, to correct any defects as they occur. This article reviews the cause of common defects in powder bed additive manufacturing, briefly surveys process monitoring strategies in the literature, and summarizes recently-developed strategies to monitor part quality during the build process. Design/methodology/approach - Factors that affect part quality in powder bed additive manufacturing are categorized as those influenced by machine variables and those affected by other build attributes. Within each category, multiple process monitoring methods are presented. Findings - A multitude of factors contribute to the overall quality of a part built using PBFAM. Rather than limiting processing to a pre-defined build recipe and assuming complete repeatability, part quality will be ensured by monitoring the process as it occurs and, when possible, altering the process conditions or build plan in real-time. Recent work shows promise in this area and brings us closer to the goal of wide-spread adoption of additive manufacturing technology. Originality/value - This work serves to introduce and define the possible sources of defects and errors in metal-based PBFAM, and surveys sensing and control methods which have recently been investigated to increase overall part quality. Emphasis has been placed on novel developments in the field and their contribution to the understanding of the additive manufacturing process.