Low-dimensional nanomaterials are zero-, one- and two-dimensional nanomaterials, in which the aspect ratio and surface-to-volume ratio vary as the dimension varies. In nanofluids, suspended nanomaterials’ movement in the base fluid can be due to Brownian motion and thermophoresis effect, which causes heat transfer. However, the emergence of nanomaterials with various dimensions has led to more advanced heat transfer mechanisms. The high aspect ratio and surface-to-volume ratio of the nanomaterials are believed to be among the factors in nanofluids’ properties enhancement. However, the morphological effect on the heat transfer enhancement in nanofluids is still ambiguous. Hence, this paper aims to explore this significant gap by reviewing the reports that investigate the effect of morphology to the heat transfer enhancement in nanofluids containing low-dimensional nanomaterials and observe the trend. The heat transfer mechanisms in nanofluids are discussed to improve understanding of the phenomena, including its methods of study. This review also includes the material characterization techniques since these approaches can provide morphological information; hence, heat transfer can be studied. Heat transfer mechanisms associated with the movement of nanoparticles were the most researched mechanism, mostly by experimentations and theoretical predictions. However, there has not been a substantial amount of research linking the morphological studies to the heat transfer enhancement in nanofluids. The study of nanolayer, nanoclustering and phonon heat transport has also been made possible by recent advancements in high-performance computing applications such as molecular dynamics simulation and machine learning, offering a more efficient method for exploring novel low-dimensional nanomaterials beyond zero-dimension.