Over the past several decades, metal Additive Manufacturing (AM) has transitioned from a rapid prototyping method to a viable manufacturing tool. AM technologies can produce parts on-demand, repair damaged components, and provide an increased freedom of design not previously attainable by traditional manufacturing techniques. The increasing maturation of metal AM is attracting high-value industries to directly produce components for use in aerospace, automotive, biomedical, and energy fields. Two leading processes for metal part production are Powder Bed Fusion with laser beam (PBF-LB/M) and Directed Energy Deposition with laser beam (DED-LB/M). Despite the many advances made with these technologies, the highly dynamic nature of the process frequently results in the formation of defects. These technologies are also notoriously difficult to control, and the existing machines do not offer closed loop control. In the present work, the application of various Machine Learning (ML) approaches and in-situ monitoring technologies for the purpose of defect detection are reviewed. The potential of these methods for enabling process control implementation is discussed. We provide a critical review of trends in the usage of data structures and ML algorithms and compare the capabilities of different sensing technologies and their application to monitoring tasks in laser metal AM. The future direction of this field is then discussed, and recommendations for further research are provided. Graphical abstract