  The features of electromagnetic processes are considered which connected with
finite size of space region in which final particles (photon, electron-positron
pair) are formed. The longitudinal dimension of the region is known as the
formation length. If some external agent is acting on an electron while
traveling this distance the emission process can be disrupted. There are
different agents: multiple scattering of projectile, polarization of a medium,
action of external fields, etc. The theory of radiation under influence of the
multiple scattering, the Landau-Pomeranchuk-Migdal (LPM) effect, is presented.
The probability of radiation is calculated with an accuracy up to "next to
leading logarithm" and with the Coulomb corrections taken into account. The
integral characteristics of bremsstrahlung are given, it is shown that the
effective radiation length increases due to the LPM effect at high energy. The
LPM effect for pair creation is also presented. The multiple scattering
influences also on radiative corrections in a medium (and an external field
too) including the anomalous magnetic moment of an electron and the
polarization tensor as well as coherent scattering of a photon in a Coulomb
field. The polarization of a medium alters the radiation probability in soft
part of spectrum. Specific features of radiation from a target of finite
thickness include: the boundary photon emission, interference effects for thin
target, multi-photon radiation. The experimental study of LPM effect is
described. For electron-positron colliding beams following items are discussed:
the separation of coherent and incoherent mechanisms of radiation, the
beam-size effect in bremsstrahlung, coherent radiation and mechanisms of
electron-positron creation.
