Additive manufacturing, which is referred to as 3D printing, is a new developed process of fabricating metallic, ceramic, plastic and concrete materials. The goal of this article is to provide an overview of 3D printing processing methods and discuss their pros and cons. A comparison with other technologies such as injection molding and cutting-based machinery was discussed. Various modeling approaches and tools at all scale levels were depicted. We have presented a case study concerning the effect of pores formation in the mechanical properties of 3D printed polymer composites using FDM process. The mechanical behavior of 3D printed composites was determined using the homogenization technique based on the RVE notion. Recent uses of this technology in the area of electronics, aerospace and biomedical engineering were highlighted. Finally, important benefits and limitations were identified in order to clarify and motivate future works in this field.