Cosmological processes are traditionally modelled via linear
perturbation theory around the Friedmann-Lemaître-Robertson-Walker class
on scales larger than a few hundred Megaparsec, combined with nonlinear
Newtonian gravity below this scale. Few treatments exist of the
nonlinear relativistic regime, and their application is generally
limited to toy models with a high degree of symmetry.
In this talk, I will review the recent application of numerical
relativity to the study of this regime in more general settings. After
an introduction to the techniques of numerical relativity, I will
describe several cosmological models where nonlinear relativistic
effects impact on major physical properties, such as the rate of
expansion, the collapse of gravitational structures, and the propagation
of light.