Lightning phenomena, plasma processing, plasma medicine and high voltage technology are governed by similar physical mechanisms. These mechanisms evolve on multiple scales in space and time, frequently ordered in a hierarchical structure. A main focus of the Multiscale Dynamics group at CWI is a better understanding of rapidly pulsed discharges in air and other media (streamers, leaders, nanosecond pulsed discharges, plasma bullets, terrestrial gamma-ray flashes, transient luminous events etc.), in collaboration with colleagues in plasma physics, electrical and mechanical engineering, atmospheric electricity and cosmic particle physics. Experimental investigations, theory and numerical simulations complement each other in providing a route to understanding.