The main objective of this research is to review and investigate the influence of carbon nanotube structure on the properties of carbon nanotube and carbon nanotube-reinforced epoxy. Carbon nanotube and carbon nanotube-reinforced epoxy are currently being frequently used in many applications such as aerospace, automotive, and electronics industries due to their excellent properties such as high tensile strength, high Young’s modulus, and electrical and thermal conductivity. In this study, the obstacles to apply carbon nanotubes as fibers within the matrix have been introduced and discussed. Additionally, the epoxy properties and application have been cited, and failure mechanisms of carbon nanotube-reinforced epoxy and geometries of carbon nanotubes have been reviewed. Furthermore, with using experimental data and applying an analytical method, the effect of carbon nanotube diameter on interlaminar shear stress within the carbon nanotube-reinforced epoxy interface has been evaluated. Additionally, the effect of temperature variation on the value of interlaminar shear stress within the single-walled carbon nanotube-reinforced epoxy interface has been discussed. Finally, the influence of the number of hexagons in the unit cell on the Young’s modulus of zigzag and armchair single-walled carbon nanotubes has been evaluated.