An extrusion based additive manufacturing (EAM) technique, recently became competitive for the rapid production of metals and ceramics components. This is made possible by extruding the metal or ceramic material in solid powder form, mixed with a binder, i.e. an expendable viscous fluid, which is removed from the part after 3D printing. The strength of these technologies relies on the large design freedom allowed by and by the cost efficiency advantage vs. alternative metal additive manufacturing processes based on high energy beams, e.g. laser/electron beam.EAM of metals and ceramics is not yet widespread, and the published scientific and technical literature is rapidly growing, but still less extensive than the literature on FDM of plastics or SLM of metals. This paper aims at filling this gap. Fused Deposition Modeling (FDM) and Powder Injection Molding (PIM) are identified as preceding or enabling technologies for EAM. This paper systematically reviews all the aspects of feedstock extrusion-based AM processes used for production of complex shaped parts. Then, the unique characteristics and advantages of the process are discussed, with respect to materials and process steps. The key process parameters are explained to illustrate the suitability of the process for diverse domains of applications.