In recent years, the nanofluids (NFs) have become the main candidates for improving or even replacing traditional heat transfer fluids. The possibility of NFs to be used in various technological applications, from renewable energies to nanomedicine, has made NFs and their thermal conductivity one of the most studied topics nowadays. Hence, this review presents an overview of the most important advances and controversial results related to the NFs thermal conductivity. The different techniques used to measure the thermal conductivity of NFs are discussed. Moreover, the fundamental parameters that affect the NFs thermal conductivity are analyzed, and possible improvements are addressed, such as the increase of long-term stability of the nanoparticles (NPs).The most representative prediction classical models based on fluid mechanics, thermodynamics, and experimental fittings are presented. Also, the recent statistical machine learning-based prediction models are comprehensively addressed, and the comparison with the classical empirical ones is made, whenever possible.