Motivated by the widespread and contradictory results regarding the glass transition temperature of carbon nanotube (CNT)/epoxy composites, we reviewed and analyzed the literature results dealing with the effect of unmodified multiwall carbon nanotubes (MWNT) on the cure behaviour of an epoxy resin (as a possible source of this discrepancy). The aim of this work was to clarify the effective role of unmodified multiwall carbon nanotubes on the cure kinetics and glass transition temperature (Tg) of their epoxy composites. It was found that various authors reported an acceleration effect of CNT. The cure reaction was promoted in its early stage which may be due to the catalyst particles present in the CNT raw material. While SWNT may lead to a decrease of Tg due to their bundling tendency, results reported for MWNT suggested an increased or unchanged Tg of the composites. The present status of the literature does not allow to isolate the effect of MWNT on the Tg due to the lack of a study providing essential information such as CNT purity, glass transition temperature along with the corresponding cure degree.