  Nonlinear heat transfer can be exploited to reveal novel transport phenomena
and thus enhance peo-ple's ability to manipulate heat flux at will. However,
there hasn't been a mature discipline called nonlinear thermotics like its
counterpart in optics or acoustics to make a systematic summary of rele-vant
researches. In the current review, we focus on recent progress in an important
part of nonlinear heat transfer, i.e., tailoring nonlinear thermal devices and
metamaterials under the Fourier's law, especially with temperature-dependent
thermal conductivities. We will present the basic designing techniques
including solving the equation directly and the transformation theory. Tuning
nonlinearity coming from multi-physical effects, and how to calculate effective
properties of nonlinear conductive composites using the effective medium theory
are also included. Based on these theories, researchers have successfully
designed various functional materials and devices such as the thermal diodes,
thermal transistors, thermal memory elements, energy-free thermostats, and
intelligent thermal materials, and some of them have also been realized in
experiments. Further, these phenomenological works can provide a feasible route
for the development of nonlinear thermotics.
