Fused Filament Fabrication (FFF) is a rapidly growing and widely used 3D printing process with many practical applications thanks to its superior advantages such as ease of handling, cost-efficiency, and ability to fabricate complex structures with reduced waste and shorter production time. However, the mechanical property deficiency and related anisotropy with respect to build direction of FFF printed parts is still one of the most crucial challenges due to inherent process limitations and material properties, resulting in internal defects in printed structures. This review article offers researchers and users in the FFF community guidance to evaluate and determine impactful methods for manufacturing polymer printed parts with required mechanical strength for a wide range of end-use applications. The paper categorizes, evaluates, and compares a large number of recent publications presenting tensile property improvements of FFF printed parts in longitudinal and transverse directions covering material development, post-treatment, and process modification. Moreover, reported tensile test results are normalised via a calculated improvement efficiency index, and fundamental mechanisms responsible for strength improvements are highlighted. The advantages of and remaining concerns for the respective approaches are then discussed and compared via their respective improvement efficiency indices, thereby highlighting the impact of the proposed evaluation approach.