Energy transport theories are being revisited at the nanoscale, as macroscopic laws known for a century are broken at dimensions smaller than those associated with energy carriers. For thermal radiation, where the typical dimension is provided by Wien's wavelength, Planck's law and associated concepts describing surface-to-surface radiative transfer have to be replaced by a full electromagnetic framework capturing near-field radiative heat transfer (photon tunnelling between close bodies), interference effects and sub-wavelength thermal emission (emitting body of small size). It is only during the last decade that nanotechnology has allowed for many experimental verifications - with a recent boom - of the large increase of radiative heat transfer at the nanoscale. In this minireview, we highlight the parameter space that has been investigated until now, showing that it is limited in terms of inter-body distance, temperature and object size, and provide clues about possible thermal-energy harvesting, sensing and management applications. We also provide an outlook on open topics, underlining some difficulties in applying single-wavelength approaches to broadband thermal emitters while acknowledging the promise of thermal nanophotonics and observing that molecular/chemical viewpoints have been hardly addressed.