Currently; the transfer of new technologies makes it necessary to also control heat transfer in different industrial processes—both in practical and research—applications. Not so long ago water and ethylene glycol were the most frequently used media in heat transfer. However, due to their relatively low thermal conductivity, they cannot provide the fast and effective heat transfer necessary in modern equipment. To improve the heat transfer rate different additives to the base liquid are sought, e.g., nanoadditives that create mono and hybrid nanofluids with very high thermal conductivity. The number of scientific studies and publications concerning hybrid nanofluids is growing, although they still represent a small percentage of all papers on nanofluids (in 2013 it was only 0.6%, and in 2017—ca. 3%). The most important point of this paper is to discuss different ways of stabilizing nanofluids, which seems to be one of the most challenging tasks in nanofluid treatment. Other future challenges concerning mono and hybrid nanofluids are also thoroughly discussed. Moreover, a quality assessment of nanofluid preparation is also presented. Thermal conductivity models are specified as well and new representative mono and hybrid nanofluids are proposed.