Although we happen to live in a universe where the CMB is highly isotropic, this observation alone does not rule out the possibility that our background spacetime is anisotropic. There are two possibilities in this regard: either there exists a marginal level of anisotropy hidden bellow the typical 0.001% fluctuations of CMB, or we inhabit a universe where CMB looks isotropic, but our background spacetime does not. In this talk I will present two anisotropic cosmological models where these possibilities hold, and show how they can be linked to current cosmological observations. It is hoped that, in face of existing and forthcoming observational data, these results can shed light on the deep questions of geometry and topology of the Universe at large scales.