Two-dimensional boron is promising as a tunable monolayer metal for nano-optoelectronics. We study the optoelectronic properties of two likely allotropes of two-dimensional boron, β12 and δ6, using first-principles density functional theory and many-body perturbation theory. We find that both systems are anisotropic metals, with strong energy- and thickness-dependent optical transparency and a weak (<1%) absorbance in the visible range. Additionally, using state-of-the-art methods for the description of the electron–phonon and electron–electron interactions, we show that the electrical conductivity is limited by electron–phonon interactions. Our results indicate that both structures are suitable as a transparent electrode.