Convection heat transfer in cavities has attracted much attention from researchers. Many kinds of nanofluids have exhibited non-Newtonian behavior and been employed as heat transfer fluids in cavities. In a non-Newtonian fluid, shear stress and strain do not have a linear relationship. Such fluids do not follow Newton’s law of shear stress. As a result, researchers have used such models as the power-law or Bingham to formulate the behavior of non-Newtonian fluids and provide a numerical solution. In this study, first the non-Newtonian nanofluids were summarized. And then two well-known models, namely the power-law and Bingham models, are introduced, which was followed by empirical studies in non-Newtonian fluids or nanofluids. Then a summary of studies on nanofluids and non-Newtonian fluids inside different types of cavities was provided. Moreover, some tables are presented summarizing numerical studies into cavities containing nanofluids or non-Newtonian fluids and their significant findings.