The motion of electrons inside atoms and molecules occurs with awesome rapidity. Quantum mechanics predicts that the electron (in the language of quantum mechanics, the electron wavepacket) of a hydrogen atom takes about 400 attoseconds (1 as = 10−18 s) to perform an oscillation around the nucleus when it is most closely bound to it. The electron wavepacket on a molecular orbit binding two hydrogen atoms together to form a molecule takes approximately the same time to circle around the hydrogen nuclei. No one has ever been able to observe these hyperfast electron motions in real time. Attosecond pulses open up this prospect.