Electron magnetohydrodynamics is a new branch of theoretical plasma ph
ysics with many applications to problems of pulsed plasmas and control
led magnetic fusion, astrophysics and physics of solids. EMH is the mu
lticomponent MHD theory reduced, in the limit of short space and time
scales and/or strong fields and high currents, to a form of electron h
ydrodynamics on a background of immovable ions. It is, in essence, hyd
rodynamic theory based on quasi-neutrality, the Hall effect and neglig
ible ion motion. Many well-known MHD effects should be revised within
the framework of EMH. Diamagnetic properties of quasi-steady plasma ba
sed on MHD theory are transformed into paramagnetism. In particular, i
nstead of field diffusion, the result is magnetic field penetration in
to a conducting medium in the form of a shock wave. The ''classical''
skin problem with an oscillating field as a boundary condition has a n
onclassical solution, demonstrating detection instead of the skin effe
ct. Some new classes of instabilities have to be taken into account. T
hese instabilities are faster than those resulting from MHD; hence, th
ey are more effective in magnetic field reconnection and enhanced ther
mal conductivity. Nontrivial electron streams become possible in thin
films, modifying their screen properties. In both Z-pinch and plasma d
iode, EMH dynamics result in some specific resistance of universal for
m. EMH effects are responsible for all aspects of plasma switching in
the conductivity phase.