Research and development in the field of structural composites have explored various combinations of materials and methods to fulfill the load-bearing demands of industries such as automotive, aerospace, military, civil, and construction. Continuous fiber-reinforced composites based on epoxy are extensively used for primary load-bearing structural applications, owing to their unique characteristics and abilities compared to their counterparts with other polymers, thermosets in particular. With the introduction of nanotechnology and the resultant development of a new class of materials called nanomaterials, it has been observed that various properties of composites can be enhanced by the incorporation of these materials into composites. Different nanofiller materials have different effects on composite properties. This review focuses on a survey of literature published over the last two decades in which nanofillers were utilized to enhance the structural properties of epoxy-based fiber-reinforced composites. Composite modifications using carbon-based nanomaterials (fullerenes, carbon nanotubes, carbon nanofibers, graphene nanoplatelets, graphene oxide), nanosilica, nanoclay, etc. are discussed in detail. A brief summary of the use of a combination of nanofillers and attempts on the modification of reinforcement fabric is also presented.