We present a first-principles density-functional study of the structural, electronic, and magnetic properties of the ferroelectric domain walls in multiferroic ${\text{BiFeO}}_3$. We find that domain walls in which the rotations of the oxygen octahedra do not change their phase when the polarization reorients are the most favorable and of these, the $109°$ domain wall centered around the BiO plane has the lowest energy. The $109°$ and $180°$ walls have a significant change in the component of their polarization perpendicular to the wall; the corresponding step in the electrostatic potential is consistent with a recent report of electrical conductivity at the domain walls. Finally, we show that changes in the Fe-O-Fe bond angles at the domain walls cause changes in the canting of the Fe magnetic moments which can enhance the local magnetization at the domain walls.