Shock waves and solitons were obtained in 2D complex plasmas i.e. plasmas mixed with micron‐sized particles. These particles acquire large (1000 – 50000e) negative charges and strongly interact with each other. The particle cloud can form ordered structures and exist in a solid, liquid, or gaseous state. A monolayer hexagonal lattice was formed from monodisperse plastic micro‐spheres in the sheath of an rf discharge and excited with an electrostatic pulse. It was found that weak pulses produced solitons, which did not change the phase state of the lattice. Stronger excitation created shock waves. The lattice melted behind the shock front and later recrystallized. Two shock regimes were distinguished. One had a stable, thin, well defined front, the other had an unstable front. The shocks were analyzed by tracking individual particles with a video camera and calculating their velocity, number density, kinetic temperature, and defect density. Molecular dynamics simulation reproduced the experimental results. Shock waves were also observed in a 3D complex plasma on board of the International Space Station. Those shocks were accompanied by a potential drop across the front. In this case not only the dust component but also ions, electrons and neutrals had to be considered. © 2004 American Institute of Physics