We study the band structure of twinned and detwinned BaFe2As2 using angle-resolved photoemission spectroscopy. The combination of measurements in the ordered and normal states along four high-symmetry momentum directions $\Gamma$ / Z − X / Y enables us to identify the complex reconstructed band structure in the ordered state in great detail. We clearly observe the nematic splitting of the dxz and dyz orbitals as well as folding due to magnetic order with a wave vector of ( π , π , π). We are able to assign all observed bands. In particular we suggest an assignment of the electron bands different from previous reports. The high-quality spectra allow us to achieve a comprehensive understanding of the band structure of BaFe2As2.