  Since the discovery of electron-wave duality, electron scattering
instrumentation has developed into a powerful array of techniques for revealing
the atomic structure of matter. Beyond detecting local lattice variations in
equilibrium structures, recent research efforts have been directed towards the
long sought-after dream of visualizing the dynamic evolution of matter in
real-time. The atomic behavior at ultrafast timescales carries critical
information on phase transition and chemical reaction dynamics, the coupling of
electronic and nuclear degrees of freedom in materials and molecules, the
correlation between structure, function and previously hidden metastable or
nonequilibrium states of matter. Ultrafast electron pulses play an essential
role in this scientific endeavor, and their generation has been facilitated by
rapid technical advances in both ultrafast laser and particle accelerator
technologies. This review presents a summary of the remarkable developments in
this field over the last few decades. The physics and technology of ultrafast
electron beams is presented with an emphasis on the figures of merit most
relevant for ultrafast electron diffraction (UED) experiments. We discuss
recent developments in the generation, manipulation and characterization of
ultrashort electron beams aimed at improving the combined spatio-temporal
resolution of these measurements. The fundamentals of electron scattering from
atomic matter and the theoretical frameworks for retrieving dynamic structural
information from solid-state and gas-phase samples are described, together with
essential experimental techniques and several landmark works. Ultrafast
electron probes with ever improving capabilities, combined with other
complementary photon-based or spectroscopic approaches, hold tremendous
potential for revolutionizing our ability to observe and understand energy and
matter at atomic scales.
