The authors study by direct numerical simulations the motion of buoyant deformable bubbles in a homogeneous flow, where the effects of viscosity, inertia, interface deformation and surface tension are all accounted for. The results are compared with the corresponding results for spherical bubbles. The microstructure of the bubble suspension is analyzed, and an explanation is proposed for the formation of these streams. Moreover, the dispersion of the bubbles and the velocity fluctuations in the liquid phase are analyzed.