  Many slope filtrations occur in algebraic geometry, asymptotic analysis,
ramification theory, p-adic theories, geometry of numbers... These functorial
filtrations, which are indexed by rational (or sometimes real) numbers, have a
lot of common properties.
  We propose a unified abstract treatment of slope filtrations, and survey how
new ties between different domains have been woven by dint of deep
correspondences between different concrete slope filtrations.
