The paradigm of slow-roll inflation provides a picture of the early universe that is in good agreement with present observations. Despite its success, most of the models studied so far rely heavily on the assumption that the universe is perfectly isotropic at early times. In this talk, I introduce cosmological perturbation theory in anisotropic inflationary models in classical general relativity, and then extend the discussion to anisotropic loop quantum cosmology, with a well-defined dynamics at Planck scales. Here, gauge-invariant perturbations are Fock quantized and evolved through an effective anisotropic bounce. Despite anisotropies die out very rapidly just before the inflationary expansion, quantum cosmological perturbations keep memory of that anisotropic phase, and leave anomalies in the Cosmic Microwave Background (CMB). With these imprints and current data, we constrain the departure from spatial isotropy of the early universe, as well as discuss new features in the angular correlation functions that are otherwise forbidden in the standard isotropic scenario.