Hierarchical design down to the nanoscale has become possible in structural composite materials with the discovery of carbon nanomaterials such as carbon nanotubes (CNTs) and graphene. Composites that simultaneously combine microscopic continuous fibers and nanoscale reinforcements are known in the field as hierarchical or nanoengineered composites. The additional reinforcement at the nanoscale promises high-performance composites with unique combinations of mechanical properties and new functionalities. Here, we review advances in fiber-reinforced polymers modified with CNTs. Three routes for integration of CNTs in composites are discussed: deposition on fibers/plies, dispersion in the matrix, and assembly into fibers. We highlight opportunities and challenges focusing on mechanical performance and processing.