Fundamental length scales such as the mean free path and the wavelength of energy carriers – e.g. electrons, phonons or photons - fall in the range of 1 – 10000 nm with corresponding average lifetimes of the order of 1-100 picoseconds. With continuing miniaturization of the devices, as well as continuing development of the experimental techniques that make possible to probe these time and length scales, more and more deviations from the simple Fourier law of thermal transport are found. Similarly miniaturization allows manipulation of radiative transport if the feature sizes are comparable to the wavelength of photons. At the same time measuring techniques complemented by detailed simulations provide ever more nuanced understanding of the thermal transport, leading to possibility of advanced thermal management in materials and devices. Yet, there are a number of outstanding questions that are not fully resolved. Those include thermal transport in reduced dimensionality (nanowires, nanotubes, 2D materials, etc.), effect of interfaces, both intrinsic and extrinsic scattering, interplay between different scattering mechanisms, coherence of broadband spectra, and peculiar interactions between different heat carriers. Thermal transport in non-crystalline solids is also of continuing interest; those include amorphous solids, bio-molecules, polymers, as well as composite materials. Novel directions include materials with combined functionalities, such as nano-thermophotovoltaics, solar thermoelectrics, or thermal transport in ferroelectrics, which may provide a possibility for real-time control of the thermal conductivity with the external fields. Other possible topics of interest are thermal transport in the extreme environments (high pressure/temperature), non-Fourier thermal transport and conductance via other than phonon and electrons heat carriers, thermal radiation from metamaterials, nanothermodynamics.