  Fundamental assumptions which form the basis of models for large-scale
structure in the Universe are sketched in light of a Lagrangian description of
inhomogeneities. This description is introduced for Newtonian self-gravitating
flows. On its basis a Lagrangian perturbation approach is discussed and
compared with the standard Eulerian theory of gravitational instability. The
performance of Lagrangian perturbation solutions up to the third order is
demonstrated in comparison with numerical N-body simulations. First results of
this comparison are presented for large scales (PM-code) and for small scales
(tree-code).
