We measured the real-time switching of metal-oxide memristors with sub-nanosecond resolution and recorded the evolution of the current and voltage during both ON (set) and OFF (reset) events. From these we determined the dynamical behavior of the conductivity for different applied bias amplitudes. Quantitative analysis of the energy cost and switching dynamics showed 115 fJ for ON-switching and 13 pJ for OFF-switching when resistance change was limited to 200%. Results are presented that show a favorable scaling with speed in terms of energy cost and reducing unnecessary damage to the devices.