We discuss the implications of rapid (few-minute) variability in the TeV flux of blazars, which has been observed recently with the HESS and MAGIC telescopes. The variability timescales seen in PKS 2155-304 and Mrk 501 are much shorter than inferred light-crossing times at the black hole horizon, suggesting that the variability involves enhanced emission in a small region within an outflowing jet. The enhancement could be triggered by dissipation in part of the black holes magnetosphere at the base of the outflow, or else by instabilities in the jet itself. By considering the energetics of the observed flares, along with the requirement that TeV photons escape without producing pairs, we deduce that the bulk Lorentz factors in the jets must be >50. The distance of the emission region from the central black hole is less well-constrained. We discuss possible consequences for multi-wavelength observations.