Additive Manufacturing is currently growing fast, especially fused deposition modeling (FDM), also known as fused filament fabrication (FFF). When manufacturing parts use FDM, there are two key parameters—strength of the part and dimensional accuracy—that need to be considered. Although FDM is a popular technology for fabricating prototypes with complex geometry and other part product with reduced cycle time, it is also limited by several drawbacks including inadequate mechanical properties and reduced dimensional accuracy. It is evident that part qualities are greatly influenced by the various process parameters, therefore an extensive review of the effects of the following process parameters was carried out: infill density, infill patterns, extrusion temperature, layer thickness, nozzle diameter, raster angle and build orientation on the mechanical properties. It was found from the literature that layer thickness is the most important factor among the studied ones. Although manipulation of process parameters makes significant differences in the quality and mechanical properties of the printed part, the ideal combination of parameters is challenging to achieve. Hence, this study also includes the influence of pre-processing of the printed part to improve the part strength and new research trends such as, vacuum-assisted FDM that has shown to improve the quality of the printing due to improved bonding between the layers. Advances in materials and technologies that are currently under development are presented. For example, the pre-deposition heating method, using an IR lamp of other technologies, shows a positive impact on the mechanical properties of the printed parts.