While there are different types of materials that can be used in Additive Manufacturing (AM), their material properties such as strength, electrical and thermal conductivity, and optical transparency typically have inferior properties compared to conventionally manufactured counterparts due to the anisotropy caused by the layer-by-layer approach. Development of composite materials could be a way to improve the mechanical properties of components produced by Fused Deposition Modelling (FDM). Polymer nanocomposites (PNC) are polymers that have been reinforced with small quantities of nonosized particles generally having high aspect ratios. PNCs represent a radical alternative to conventional filled polymer blends. The value of PNC technology is not solely based on mechanical enhancement of the neat resin nor the direct replacement of current filler or blend materials. Rather, its importance comes from providing value-added properties not present in the neat resin. The addition of nanostructured materials into the printing media for additive manufacturing affects significantly the properties of the final parts. Challenges in the application of nanomaterials to additive manufacturing are nevertheless numerous. The main purpose of this article is to review the studies of the marriage of FDM and nanotechnology.