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Fused deposition modeling (FDM) is one of the most popular and ubiquitous additive manufacturing methods, which uses a layering procedure to build 3D models layers-upon-layers. Since the layers are the constituents of the resulted 3D part, the layering process can directly affect the part’s surface finish and mechanical properties, which are the two major drawbacks in FDM. To this end, investigating different layering/slicing algorithms can deepen the understanding of the challenges and gaps in FDM, which will help improve the quality of the 3D printed parts. In this review, slicing algorithms developed for FDM technology are categorized into two main groups: planar and nonplanar. While planar algorithms generate flat layers, nonplanar algorithms provide curved and out-of-plane layers, increasing build speed, eliminating support structures, smoothening the outer surface, and enhancing …