Additive Manufacturing (AM), commonly known as “3D printing”, is rapidly integrated into many various fields, from everyday commercial to high-end medical and aerospace. Its production flexibility in small-scale and complex shapes is a significant advantage over conventional methods. However, inferior physical properties of parts manufactured by AM in general, and by material extrusion in particular, compared to traditional fabrication methods, inhibit its full assimilation. Specifically, the mechanical properties of printed parts are not high enough and, more importantly, not consistent enough. Optimization of the many various printing parameters is therefore required. This work reviews the influence of material selection, printing parameters such as path (e.g., layer thickness and raster angle), build (e.g., infill and building orientation) and temperature parameters (e.g., nozzle or platform temperature) on mechanical properties. Moreover, this work focuses on the interactions between the printing parameters, their mechanisms, and the statistical methods required to identify such interactions. Choosing the right parameters can increase mechanical properties by up to 60% (raster angle and orientation build), or render other parameters insignificant (material selection), while specific settings of certain parameters can completely inverse the influence trend of other parameters. Finally, trends for future research are suggested.