Addition of nanoparticles into a fluid can improve the heat transfer performance of the base fluid in heat exchangers. In this work, the preparation method and process of nanofluids are introduced, and thermal properties of nanofluids, such as thermal conductivity and viscosity, are discussed deeply. This paper summarizes various theoretical models of thermal conductivity and viscosity of nanofluids. A comprehensive literature survey on applications and limitations of nanofluids has been compiled. This paper also aims to review the natural and forced convective heat transfer characteristics of nanofluids with and without magnetic fields. The discussion for the natural convective heat transfer of nanofluids focuses on the heat transfer performance of non-conventional enclosures and electric heaters. The effects on heat transfer due to variations of heated walls are also investigated. Specific applications of nanofluids in a tube with trapezoidal ribs, double-tube heat exchangers, and plate heat exchangers have been reviewed and presented in a discussion about forced convective heat transfer. The previous results show that the inlet temperature of nanofluids obviously affects the heat transfer characteristics of double-tube heat exchangers, whereas a multi-walled carbon nanotube–water nanofluid shows significant advantages in plate heat exchangers. Finally, this paper studies natural convective heat transfer of magnetic fluids in a square cavity and forced convection heat transfer in a straight tube and a corrugated structure under the action of magnetic fields. It is found that the heat transfer performance of an Fe3O4–water nanofluid is enhanced when a magnetic field is applied to the corrugated plate heat exchangers, and the pressure drop can be reduced by around 10%. It is recommended that natural convection of magnetic fluids needs to be investigated experimentally in a real cavity and a corrugated channel under the influence of a magnetic field. In addition, studies of alternating magnetic field are recommended to reveal any improvements of thermal performance of magnetic fluids in heat exchange devices. This review puts forward an effective solution for improvement of the thermal performance of heat transfer equipment and serves as a basic reference for applications of nanofluids in heat transfer fields.