There is a great need for advanced functional materials such as light-weight and high strength materials, super capacitive materials, highly conductive materials for many advanced engineering applications. Carbon nanotube (CNT)/polymer composites are a new class of materials with a wide range of properties for engineering applications. However, the major challenges for CNT/polymer composites are to attain a uniform dispersion of CNTs in polymer matrices and an efficient interfacial adhesion between CNTs and matrices. Therefore, the objective of this thesis is to fabricate CNT/polymer composites for various engineering applications using a melt-mixing technique. The modifications, such as physical and chemical functionalisations, of multiwalled carbon nanotubes (MWCNTs) were also made. The properties of the CNT/polymer composites, such as electrical, thermal, mechanical, morphological and rheological properties, and the relevant mechanisms have been studied systematically. The improved interfacial adhesion between MWCNTs and a matrix polymer as well as the uniform dispersion of MWCNTs in the polymer matrix were achieved by means of functionalisations of MWCNTs. Moreover, a complementary effect between MWCNTs and conductive carbon black (CCB) was found to promote the formation of electrically conductive network of the carbon fillers in the polymer matrix, resulting in a dramatic increase in the electrical conductivity of the resultant composites.