The increase in accessibility of fused filament fabrication (FFF) machines has inspired the scientific community to work towards the understanding of the structural performance of components fabricated with this technology. Numerous attempts to characterize and to estimate the mechanical properties of structures fabricated with FFF have been reported in the literature. Experimental characterization of printed components has been reported extensively. However, few attempts have been made to predict properties of printed structures with computational models, and a lot less work with analytical approximations. As a result, a thorough review of reported experimental characterization and predictive models is presented with the aim of summarizing applicability and limitations of those approaches. Finally, recommendations on practices for characterizing printed materials are given and areas that deserve further research are proposed.