  We present a review of vector field models of inflation and, in particular,
of the statistical anisotropy and non-Gaussianity predictions of models with
SU(2) vector multiplets. Non-Abelian gauge groups introduce a richer amount of
predictions compared to the Abelian ones, mostly because of the presence of
vector fields self-interactions. Primordial vector fields can violate isotropy
leaving their imprint in the comoving curvature fluctuations zeta at late
times. We provide the analytic expressions of the correlation functions of zeta
up to fourth order and an analysis of their amplitudes and shapes. The
statistical anisotropy signatures expected in these models are important and,
potentially, the anisotropic contributions to the bispectrum and the
trispectrum can overcome the isotropic parts.
