Current article outlines the latest research of high CNTs thermal conductivities and their nanofluids. Because of their exceptional structure and small size, carbon nanotubes has thermal properties enabling them to be an ideal material in the investigation of thermal controlling, both on the micro- and the macro-scales and low-dimensional phonon physics researches. Depending on the process parameters used in CNTs synthesis, the thermal conduction properties are notably affected by the alteration of the diameter, the chirality, the length, and the quality of CNTs. This review elucidates in details the necessity of thermal conductivity on several factors including the aspect of tubes, number of defects, morphology, atomic arrangement and the occurrence of impurities. Besides these factors, the dependence of thermal conductivity on chirality and temperature is also discussed. Several experimental investigations and theoretical models to estimate thermal conductivity of CNTs and their nanomaterial are also reviewed. This review also elucidates different models suggested by researchers for estimating properties of CNT-based nanofluids. •High thermal conductivities of CNT are examined.•Thermal conduction properties are notably affected by the alteration of the diameter.•Dependence of thermal conductivity on temperature and chirality was discussed.