Carbon nanotubes (CNTs), with unique graphitic structure, superior mechanical, electrical, optical and biological properties, has attracted more and more interests in biomedical applications, including gene/drug delivery, bioimaging, biosensor and tissue engineering. In this review, we focus on the role of CNTs and their polymeric composites in tissue engineering applications, with emphasis on their usages in the nerve, cardiac and bone tissue regenerations. The intrinsic natures of CNTs including their physical and chemical properties are first introduced, explaining the structure effects on CNTs electrical conductivity and various functionalization of CNTs to improve their hydrophobic characteristics. Biosafety issues of CNTs are also discussed in detail including the potential reasons to induce the toxicity and their potential strategies to minimise the toxicity effects. Several processing strategies including solution-based processing, polymerization, melt-based processing and grafting methods are presented to show the 2D/3D construct formations using the polymeric composite containing CNTs. For the sake of improving mechanical, electrical and biological properties and minimising the potential toxicity effects, recent advances using polymer/CNT composite the tissue engineering applications are displayed and they are mainly used in the neural tissue (to improve electrical conductivity and biological properties), cardiac tissue (to improve electrical, elastic properties and biological properties) and bone tissue (to improve mechanical properties and biological properties). Current limitations of CNTs in the tissue engineering are discussed and the corresponded future prospective are also provided. Overall, this review indicates that CNTs are promising “next-generation” materials for future biomedical applications.