Developments in the synthesis and scalable manufacturing of carbon nanomaterials like carbon nanotubes (CNTs) have been widely used in the polymer material industry over the last few decades, resulting in a series of fascinating multifunctional composites used in fields ranging from portable electronic devices, entertainment and sports to the military, aerospace, and automotive sectors. CNTs offer good thermal and electrical properties, as well as a low density and a high Young’s modulus, making them suitable nanofillers for polymer composites. As mechanical reinforcements for structural applications CNTs are unique due to their nano-dimensions and size, as well as their incredible strength. Although a large number of studies have been conducted on these novel materials, there have only been a few reviews published on their mechanical performance in polymer composites. As a result, in this review we have covered some of the key application factors as well as the mechanical properties of CNTs-reinforced polymer composites. Finally, the potential uses of CNTs hybridised with polymer composites reinforced with natural fibres such as kenaf fibre, oil palm empty fruit bunch (OPEFB) fibre, bamboo fibre, and sugar palm fibre have been highlighted.