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By additive manufacturing technologies, an object is produced deposing material layer by layer. The piece grows along the build direction, which is one of the main manufacturing parameters of Additive Manufacturing (AM) technologies to be set-up. This process parameter affects the cost, quality, and other important properties of the manufactured object. In this paper, the Objective Functions (OFs), presented in the literature for the search of the optimal build direction, are considered and reviewed. The following OFs are discussed: part quality, surface quality, support structure, build time, manufacturing cost, and mechanical properties. All of them are distinguished factors that are affected by build direction. In the first part of the paper, a collection of the most significant published methods for the estimation of the factors that most influence the build direction is presented. In the second part, a summary of the optimization techniques adopted from the reviewed papers is presented. Finally, the advantages and disadvantages are briefly discussed and some possible new fields of exploration are proposed.