Inflation prescribes a homogenous and isotropic universe on large scales, and it generates density fluctuations which are expected to be spatially correlated over the whole Hubble volume. Such fundamental predictions have been tested with current Cosmic Microwave Background (CMB) data and found to be in tension with our — remarkably simple — ΛCDM model. Is it just a random fluke or a fundamental issue with the present model? In this talk, I will present new possibilities of using CMB polarization as a probe of the measured suppression of the large-scale temperature correlation function. I will also discuss the viability of using this new technique with present and upcoming data. To further analyze the statistical properties of the CMB temperature sky, I will show results from our latest analysis focused on constraining the degree of statistical anisotropy of the CMB in the context of the observed large-scale dipole power asymmetry. I will also highlight future prospects for improving the current analysis.