Engineering of cooling mechanism is of primary importance for the development of nanoelectronics. Whereas radiation cooling is rather inefficient in nowadays electronic devices, the strong anisotropy of 2D materials allows for enhanced efficiency because their hyperbolic electromagnetic dispersion near phonon resonances allows them to sustain much larger (∼ 10 5) number of radiating channels. In this review, we address radiation cooling in 2D materials, specifically graphene hexagonal boron nitride (hBN) heterostructures. We present the hyperbolic dispersion of electromagnetic waves due to anisotropy, and describe how the spontaneous fluctuations of current in a 2D electronic channel can radiate thermal energy in its hyperbolic surrounding medium. We show that both the regime of (i) thermal current fluctuations and (ii) out-of-equilibrium current fluctuations can be described within the framework of transmission line theory leading to (i) superPlanckian thermal emission and (ii) electroluminescent cooling. We discuss a recent experimental investigation on graphene-on-hBN transistors using electronic noise thermometry. In a high mobility semimetal like graphene at large bias, a steady-state out-of-equilibrium situation is caused by the constant Zener tunneling of electrons opening a route for electroluminescence of hyperbolic electromagnetic modes. Experiments reveal that, compared to superPlanckian thermal emission, electroluminescent cooling is particularly prominent once the Zener tunneling regime is reached: observed cooling powers are nine orders of magnitude larger than in conventional LEDs.