  We review recent developments in nonlinear quantum transport through
nanostructures and mesoscopic systems driven by thermal gradients or in
combination with voltage biases. Low-dimensional conductors are excellent
platforms to analyze both the thermoelectric and heat dynamics beyond linear
response because due to their small size a small temperature difference applied
across regions gives rise to large thermal biases. We offer a theoretical
discussion based on the scattering approach to highlight the differences
between the linear and the nonlinear regimes of transport. We discuss recent
experiments on quantum dots and molecular junctions subjected to strong
temperature differences. Theoretical predictions concerning the Kondo effect
and heat rectification proposals are briefly examined. An important issue is
the calculation of thermoelectric efficiencies including nonlinearities. Cross
Seebeck effects and nonlinear spin filtering arise in superconductors and
topological insulators while mixed noises between charge and heat currents are
also considered. Finally, we provide an outlook on the possible future
directions of the field.
