In metal additive manufacturing (AM), rapid material temperature changes and complicated material behavior inevitably lead to various types of surface and internal defects, which are detrimental to the performance of final parts, and hinder the development and application of metal AM in key areas. Acquiring defect information in time is beneficial for adjusting process parameters, improving manufacturing process, and elevating parts quality. Meanwhile, the defect information can be utilized to conduct subsequent machining and processing. Therefore, it is of significance to conduct research on defect detection technologies to improve AM technology and expand its applications. To resolve this issue, this paper introduces the common defects in AM parts and summarizes their origins. Then typical studies on AM defect detection technologies in recent years are reviewed, with a focus on the monitoring of process signatures and the online non-destructive testing methods. The application scope of different methods is also presented. Finally, the development trend of defect detection technology is forecasted. A conclusion is drawn that defects in AM are complicated and the parts quality needs to be assured by detection methods and technologies. However, methods proposed so far still cannot satisfy the requirement of AM, and the technology should be developed towards integration and intelligence in the future.