Metal additive manufacturing has emerged as a new manufacturing option for aerospace and biomedical applications. The many challenges that surround this new manufacturing technology fall into several different categories. The paper addresses one of these categories, the physical mechanisms that control the additive manufacturing process. Physical mechanisms control the effects of processing parameters on microstructures and properties of additively manufactured parts. Some mechanisms might not have been recognized, yet, and for those that are currently known, detailed quantitative predictions have to be established. The physical mechanisms of metal additive manufacturing are firmly grounded in metallurgy, branching into laser physics and the physics of granular materials. Powder bed additive manufacturing is described from the powder storage to post-processing and elements of metallurgy are highlighted that are relevant for the different aspects of the additive manufacturing process. These elements include the surface reactions on powder particles, the heating and melting behavior of the powder bed, solidification, and post-processing. This overview of the different metallurgical aspects to additive manufacturing is intended to help guide research efforts and it will also serve as a snapshot of the current understanding of powder bed additive manufacturing.