In systems with a broken time-reversal symmetry, Lorentz reciprocity no longer applies. Such systems can include magneto-optical materials, for example, in which the time-reversal symmetry is broken by applying an external magnetic field, which induces special so-called non-reciprocal optical properties. If, for example, consider a magneto-optical nanoparticle with an applied magnetic field that radiates heat into its environment, you will find a circular heat flow around this particle or a circularly polarized heat radiation, which also results in an angular momentum and spin of the fluctuating field. This effect can be traced back to the Lorentz force acting on the electrons in the nanoparticle. It provides the basis for understanding the thermal Hall effect for thermal radiation, non-reciprocal heat transfer using non-reciprocal surface waves and other related phenomena. In particular, we investigate the influence of non-reciprocal material properties on thermal transport by thermal radiation in nanoscopic many-body systems.