The structure of 208Po populated through the EC/β+ decay of 208At is investigated using γ-ray spectroscopy at the ISOLDE Decay Station. The presented level scheme contains 27 new excited states and 43 new transitions, as well as a further 50 previously observed γ rays which have been (re)assigned a position. The level scheme is compared to shell model calculations. Through this analysis approximately half of the β-decay strength of 208At is found to proceed via allowed decay and half via first-forbidden decay. The first-forbidden transitions predominantly populate core excited states at high excitation energies, which is qualitatively understood using shell model considerations. This mass region provides an excellent testing ground for the competition between allowed and first-forbidden β-decay calculations, important for the detailed understanding of the nucleosynthesis of heavy elements.