•Systematic review of machine learning (ML) in metal additive manufacturing.•Discussion of the shift from ML to physics-informed machine learning (PIML).•Discussion of the challenges of PIML in metal additive manufacturing.•Proposal of open questions to encourage future research. Machine learning (ML) has shown to be an effective alternative to physical models for quality prediction and process optimization of metal additive manufacturing (AM). However, the inherent “black box” nature of ML techniques such as those represented by artificial neural networks has often presented a challenge to interpret ML outcomes in the framework of the complex thermodynamics that govern AM. While the practical benefits of ML provide an adequate justification, its utility as a reliable modeling tool is ultimately reliant on assured consistency with physical principles and model transparency. To facilitate the fundamental needs, physics-informed machine learning (PIML) has emerged as a hybrid machine learning paradigm that imbues ML models with physical domain knowledge such as thermomechanical laws and constraints. The distinguishing feature of PIML is the synergistic integration of data-driven methods that reflect system dynamics in real-time with the governing physics underlying AM. In this paper, the current state-of-the-art in metal AM is reviewed and opportunities for a paradigm shift to PIML are discussed, thereby identifying relevant future research directions.