Due to the unique properties of carbon nanotubes (CNTs), the electrical and thermal conductivity of CNT-modified polymeric composites (CNTMPCs) can be manipulated and depend on several factors. There are many factors that affect the thermal and electrical conductivity of CNTs and CNTMPCs, such as chirality, length, type of CNTs, fabrication, surface treatment, matrix and interfacial interaction between the matrix and reinforcement (CNTs). This paper reviews the research on molecular dynamics (MD) simulations of the effects of some factors affecting the thermal and electrical conductivity of CNTs and CNTMPCs. First, the chirality dependence of the thermal and electrical conductivity of single-walled carbon nanotubes (SWNTs) was analyzed. The effect of chirality on the conductivity of short-length CNTs is greater than that of long-length CNTs, and the larger the chiral angle, the greater the conductivity of the CNTs. Furthermore, the thermal and electrical conductivity of the zigzag CNTs is smaller than that of the armchair one. Therefore, as the tube aspect ratio becomes longer and conductivity increases, while the effect of chirality on the conductivity decreases. In addition, hydrogen bonding affects the electrical and thermal conductivity of the CNTMPCs. The modeling of SWNTs shows that the thermal and electrical conductivity increases significantly with increasing overlap length. MD simulations can be effectively used to design highly conductive CNTMPCs with appropriated thermal and electrical properties. Since there are too many factors affecting the thermal and electrical conductivity of CNTMPCs, this paper only reviews the effects of limited factors on the thermal and electrical conductivity of CNTs and CNTMPCs based on MD simulations, and further detailed studies are required.