  Colliding high energy hadrons either produce new particles or scatter
elastically with their quantum numbers conserved and no other particles
produced. We consider the latter case here. Although inelastic processes
dominate at high energies, elastic scattering contributes considerably (18-25%)
to the total cross section. Its share first decreases and then increases at
higher energies. Small-angle scattering prevails at all energies. Some
characteristic features are seen that provide informationon the geometrical
structure of the colliding particles and the relevant dynamical mechanisms. The
steep Gaussian peak at small angles is followed by the exponential (Orear)
regime with some shoulders and dips, and then by a power-law drop.
  Results from various theoretical approaches are compared with experimental
data. Phenomenological models claiming to describe this process are reviewed.
The unitarity condition predicts an exponential fall for the differential cross
section with an additional substructure to occur exactly between the low
momentum transfer diffraction cone and a power-law, hard parton scattering
regime under high momentum transfer. Data on the interference of the Coulomb
and nuclear parts of amplitudes at extremely small angles provide the value of
the real part of the forward scattering nuclear amplitude.
  The real part of the elastic scattering amplitude and the contribution of
inelastic processes to the imaginary part of this amplitude (the so-called
overlap function) at nonforward transferred momenta are also discussed.
Problems related to the scaling behavior of the differential cross section are
considered. The power-law regime at highest momentum transfer is briefly
described.
