  A primordial inflationary phase allows one to erase any possible anisotropic
expansion thanks to the cosmic no-hair theorem. If there is no global
anisotropic stress, then the anisotropic expansion rate tends to decrease. What
are the observational consequences of a possible early anisotropic phase? We
first review the dynamics of anisotropic universes and report analytic
approximations. We then discuss the structure of dynamical equations for
perturbations and the statistical properties of observables, as well as the
implication of a primordial anisotropy on the quantization of these
perturbations during inflation. Finally we briefly review models based on
primordial vector field which evade the cosmic no-hair theorem.
