Nonlinear heat transfer can be exploited to reveal novel transport phenomena and thus enhance people’s ability to manipulate heat flux at will. However, there has not been a mature discipline called nonlinear thermotics like its counterpart in optics or acoustics to make a systematic summary of relevant 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 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.