It is both remarkable, and disappointing, that only two parameters describing the primordial perturbations are required to explain the statistical properties of millions of CMB temperature perturbations. However, the persistence of several large-scale cosmological anomalies in WMAP and Planck satellite data may provide a clue to new physics. I will discuss how inflationary models can explain the observed dipolar power asymmetry, and the extreme difficulties of building a complete working model.