State-of-the-art microscopy and diffraction imaging provides insight into the atomic and sub-atomic structure of matter. They permit determination of the positions of atoms in a crystal lattice or in a molecule as well as the distribution of electrons inside atoms. State-of-the-art time-resolved spectroscopy with femtosecond and attosecond resolution provides access to dynamic changes in the atomic and electronic structure of matter. Our proposal aims at combining these two frontier techniques of XXI century science to make a long-standing dream of scientist come true: the direct observation of atoms and electrons in their natural state: in motion. Shifts in the atoms positions by tens to hundreds of picometers can make chemical bonds break apart or newly form, changing the structure and/or chemical composition of matter. Electronic motion on similar scales may result in the emission of light, or the initiation of processes that lead to a change in physical or chemical properties, or biological function. These motions happen within femtoseconds and attoseconds, respectively. To make them observable, we need a 4-dimensional (4D) imaging technique capable of recording freeze-frame snapshots of microscopic systems with picometer spatial resolution and femtosecond to attosecond exposure time. The motion can then be visualized by slow-motion replay of the freeze-frame shots. The goal of this project is to develop a 4D imaging technique that will ultimately offer picometer resolution is space and attosecond resolution in time.