Even if electrons are bound to atoms they can – after acquiring energy from their surroundings – change their position tremendously fast. This happens within attoseconds. Electron motion in atomic systems is at the heart of all phenomena in nature except for nuclear processes. It is, among others, responsible for the emission of light, the photosynthesis of plants, the change of molecular structure, the transport of information in our nerves and for the efficacy of radiation cancer therapy.

On the following pages we review how electrons behave in atoms, molecules, solids and plasmas. We address the relevance of electronic motion to information and medical technology. Controlling and knowing the electrons’ motion down to the atomic scale opens exciting new prospects for information technology, life science and basic energy science. To make these ultrafast movements directly observable and controllable one must be able to 'freeze' the motion, such as is done in high-speed photography. We explain how ultrashort flashes of laser light make it possible to produce freeze-frame shots of atoms and electrons and reconstruct their motion from these shots in 'slow-motion replay'.