  I review the nature of three-dimensional collapse in the Zeldovich
approximation, how it relates to the underlying nature of the three-dimensional
Lagrangian manifold and naturally gives rise to a hierarchical structure
formation scenario that progresses through collapse from voids to pancakes,
filaments and then halos. I then discuss how variations of the Zeldovich
approximation (based on the gravitational or the velocity potential) have been
used to define classifications of the cosmic large-scale structure into
dynamically distinct parts. Finally, I turn to recent efforts to devise new
approaches relying on tessellations of the Lagrangian manifold to follow the
fine-grained dynamics of the dark matter fluid into the highly non-linear
regime and both extract the maximum amount of information from existing
simulations as well as devise new simulation techniques for cold collisionless
dynamics.
