3D printing, more formally known as Additive Manufacturing (AM), is already being adopted for rapid prototyping and soon rapid manufacturing. This review provides a brief discussion about AM and also the most employed AM technologies for polymers. The commonly-used ASTM and ISO mechanical test standards which have been used by various research groups to test the strength of the 3D-printed parts have also been reported. Also a summary of an exhaustive amount of literature regarding the mechanical properties of 3D-printed parts is included. Specifically, properties under different loading types such as tensile, bending, compressive, fatigue, impact and others. Properties at low temperatures have also been discussed. Effects of fillers as well as post-processing on the mechanical properties have been discussed. Lastly, several important questions to consider in the standardization of mechanical test methods have been discussed.