Material extrusion-based additive manufacturing (ME-AM) is an emerging processing technique that is characterized by the selective deposition of thermoplastic filaments in a layer-by-layer manner based on digital part models. Recently, it has attracted considerable attention, as this technique offers manifold benefits over conventional manufacturing technologies. However, to meet the challenges of complex industrial applications, certain shortcomings of ME-AM still need to be overcome. A case in point is the limited amount of semicrystalline thermoplastics, which are still not established as reliable, commercial filament materials. Particularly, polypropylene (PP) offers attractive properties that are unique among the ME-AM material portfolio. This review describes the current approaches of fabricating PP components by ME-AM. Both commercial and scientific strategies to make PP 3D-printable are elaborated and compared. As dimensional issues are especially problematic for PP, a comprehensive section of this review focuses on the strategies developed for mitigating warpage for PP parts fabricated by ME-AM.