Hybrid additive manufacturing (hybrid-AM) has described hybrid processes and machines as well as multimaterial, multistructural, and multifunctional printing. The capabilities afforded by hybrid-AM are rewriting the design rules for materials and adding a new dimension in the design for additive manufacturing (AM) paradigm. This work primarily focuses on defining hybrid-AM in relation to hybrid manufacturing (HM) and classifying hybrid-AM processes. Hybrid-AM machines, materials, structures, and function are also discussed. Hybrid-AM processes are defined as the use of AM with one or more secondary processes or energy sources that are fully coupled and synergistically affect part quality, functionality, and/or process performance. Historically, defining HM processes centered on process improvement rather than improvements to part quality or performance; however, the primary goal for the majority of hybrid-AM processes is to improve part quality and part performance rather than improve processing. Hybrid-AM processes are typically a cyclic process chain and are distinguished from postprocessing operations that do not meet the fully coupled criterion. Secondary processes and energy sources include subtractive and transformative manufacturing technologies, such as machining, remelting, peening, rolling, and friction stir processing (FSP). As interest in hybrid-AM grows, new economic and sustainability tools are needed as well as sensing technologies that better facilitate hybrid processing. Hybrid-AM has ushered in the next evolutionary step in AM and has the potential to profoundly change the way goods are manufactured.