  We describe various expansion schemes that can be used to study gravitational
clustering. Obtained from the equations of motion or their path-integral
formulation, they provide several perturbative expansions that are organized in
different fashion or involve different partial resummations. We focus on the
two-point and three-point correlation functions, but these methods also apply
to all higher-order correlation and response functions. We present the general
formalism, which holds for the gravitational dynamics as well as for similar
models, such as the Zeldovich dynamics, that obey similar hydrodynamical
equations of motion with a quadratic nonlinearity. We give our explicit
analytical results up to one-loop order for the simpler Zeldovich dynamics. For
the gravitational dynamics, we compare our one-loop numerical results with
numerical simulations. We check that the standard perturbation theory is
recovered from the path integral by expanding over Feynman's diagrams. However,
the latter expansion is organized in a different fashion and it contains some
UV divergences that cancel out as we sum all diagrams of a given order.
Resummation schemes modify the scaling of tree and one-loop diagrams, which
exhibit the same scaling over the linear power spectrum (contrary to the
standard expansion). However, they do not significantly improve over standard
perturbation theory for the bispectrum, unless one uses accurate two-point
functions (e.g. a fit to the nonlinear power spectrum from simulations).
Extending the range of validity to smaller scales, to reach the range described
by phenomenological models, seems to require at least two-loop diagrams.
