Designing and manufacturing functional parts for fields such as engineering and medicine is a major goal of Fused Deposition Modeling (FDM). These activities should be supported by knowledge on how different settings of process parameters impact the mechanical behavior of the products. However, obtaining this information is a quite complex task given the large variety of possible combinations of materials-3D printers-slicing software-process parameters. Thus, the importance of reviewing the current research on this topic for identifying practical and useful aspects, key process parameters and limitations, but also for understanding to what extent the results of these researches are relevant and can be applied in further studies and real applications. A systematic literature search was performed based on classification according to the type of 3D printing polymer. The most significant process parameters considered as influencing FDM specimens' tensile, compression, flexural or impact strengths are discussed considering the results presented in the literature. A necessary distinction between the mechanical properties of material and testing specimens (as given by producers and by experiments) and the mechanical behavior of a FDM end-part is also made.