Purpose: The purpose of this paper is to systematically review the published slicing methods for additive manufacturing (AM), especially the multi-direction and non-layerwise slicing methods, which are particularly suitable for the directed energy deposition (DED) process to improve the surface quality and eliminate the usage of support structures. Design/methodology/approach: In this paper, the published slicing methods are clarified into three categories: the traditional slicing methods (e.g. the basic and adaptive slicing methods) performed in the powder bed fusion (PBF) system, the multi-direction slicing methods and non-layerwise slicing methods used in DED systems. The traditional slicing methods are reviewed only briefly because a review article already exists for them, and the latter two slicing methods are reviewed comprehensively with further discussion and outlook. Findings: A few traditional slicing approaches were developed in the literature, including basic and adaptive slicing methods. These methods are efficient and robust when they are performed in the PBF system. However, they are retarded in the DED process because costly support structures are required to sustain overhanging parts and their surface quality and contour accuracy are not satisfactory. This limitation has led to the development of various multi-direction and non-layerwise slicing methods to improve the surface quality and enable the production of overhangs with minimum supports. Originality/value: An original review of the AM slicing methods is provided in this paper. For the traditional slicing methods and the multi-direction and non-layerwise slicing method, the published slicing strategies are discussed and compared. Recommendations for future slicing work are also provided.