Interstellar bubbles appear to be smaller in observations than expected from calculations. Instabilities at the shell boundaries create three-dimensional (3D) effects and are probably responsible for part of this discrepancy. We investigate instabilities and dynamics in superbubbles using 3D hydrodynamics simulations with time-resolved energy input from massive stars, including supernova explosions. We find that the superbubble shells are accelerated by supernova explosions, coincident with substantial brightening in soft X-ray emission. In between the explosions, the superbubbles lose energy efficiently, approaching the momentum-conserving snowplow limit. This and enhanced radiative losses due to instabilities reduce the expansion compared to the corresponding radiative bubbles in pressure-driven snowplow models with constant energy input. We note generally good agreement with observations of superbubbles and some open issues. In particular, there are hints that the shell velocities in the X-ray-bright phases are underpredicted.