  This article reviews the different mechanisms affecting the orbits of
trans-Neptunian objects, ranging from internal perturbations (planetary
scattering, mean-motion resonances, secular effects) to external perturbations
(galactic tides, passing stars). We outline the theoretical tools that can be
used to model and study them, focussing on analytical approaches. We eventually
compare these mechanisms to the observed distinct populations of
trans-Neptunian objects and conclude on how they participate to the sculpting
of the whole distribution.
