Suspensions of nanoparticles, widely known as nanofluids, are considered as advanced heat transfer media for thermal management and conversion systems. Research on their convective thermal transport is of paramount importance for their applications in such systems such as heat exchangers and solar collectors. This paper presents experimental research on the natural convection heat transfer performances of nanofluids in different geometries from thermal management and conversion perspectives. Experimental results and available experiment-derived correlations for the natural thermal convection of nanofluids are critically analyzed. Other features such as nanofluid preparation, stability evaluation and thermophysical properties of nanofluids that are important for this thermal transfer feature are also briefly reviewed and discussed. Additionally, techniques (active and passive) employed for enhancing the thermo-convection of nanofluids in different geometries are highlighted and discussed. Hybrid nanofluids are featured in this work as the newest class of nanofluids, with particular focuses on the thermophysical properties and natural convection heat transfer performance in enclosures. It is demonstrated that there has been a lack of accurate stability evaluation given the inconsistencies of available results on these properties and features of nanofluids. Although nanofluids exhibit enhanced thermophysical properties such as viscosity and thermal conductivity, convective heat transfer coefficients were observed to deteriorate in some cases when nanofluids were used, especially for nanoparticle concentrations of more than 0.1 vol.%. However, there are inconsistencies in the literature results, and the underlying mechanisms are also not yet well-understood despite their great importance for practical applications.