Microbubble-laden homogeneous and isotropic turbulent flow is investigated by using direct numerical simulation of the three-dimensional Navier–Stokes equations and computing the bubble trajectories with Lagrangian tracking. The bubble motion is calculated by taking into account the effect of fluid acceleration plus added mass, drag, gravity, and in particular the lift force, which had been neglected in many previous simulations. By comparing the results from simulations with and without lift, we find the effect of the lift force to be crucial: for passive bubbles, i.e. bubbles without backreaction on the flow (one-way coupling), the lift enhances the accumulation of bubbles on the downward flow side of vortices, resulting in a considerably reduced rise velocity of bubbles in turbulent flow, compared to still water. This also has consequences for the active bubble case, i.e. for bubbles with backreaction on the flow (two-way coupling): the energy spectrum of the turbulence is modified {non-uniformly}. Because of the combined effect of preferential bubble clustering in downflow zones and the local buoyant transfer, which reduces the vertical fluid velocity fluctuations, large-scale motions (small wavenumbers $k$) are suppressed. In contrast, small-scale motions (large wavenumbers $k$) are enhanced due to the local bubble forcing. The net effect turns out to be a reduction of the energy dissipation rate.