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Additive manufacturing (AM) is increasingly used for fabricating parts directly from digital models, usually by depositing and bonding successive layers of various materials such as polymers, metals, ceramics, and composites. The design freedom and reduced material consumption for producing near-net-shaped components have made AM a popular choice across various industries, including the automotive and aerospace sectors. Despite its growing popularity, the accurate estimation of production time, productivity and cost remains a significant challenge due to the ambiguity surrounding the technology. Hence, reliable cost estimation models are necessary to guide decisions throughout product development activities. This paper provides a thorough analysis of the state of the art in cost models for AM with a specific focus on metal Directed Energy Deposition (DED) and Powder Bed Fusion (PBF) processes. An overview of DED and PBF processes is presented to enhance the understanding of how process parameters impact the overall cost. Consequently, suitable costing techniques and significant cost contributors in AM have been identified and examined in-depth. Existing cost modelling approaches in the field of AM are critically evaluated, leading to the suggestion of a comprehensive cost breakdown including often-overlooked aspects. This study aims to contribute to the development of accurate cost prediction models in supporting decision making in the implementation of AM. [ABSTRACT FROM AUTHOR]