Do We Really Understand the Cosmos?

Our knowledge about the universe has increased tremendously in the last three decades or so --- thanks to the progress in observations --- but our understanding has improved very little. There are several fundamental questions about our universe for which we have no answers within the current, operationally very successful, approach to cosmology. Worse still, we do not even know how to address some of these issues within the conventional approach to cosmology. This fact suggests that we are missing some important theoretical ingredients in the overall description of the cosmos. I will argue that these issues --- some of which are not fully appreciated or emphasized in the literature --- demand a paradigm shift: We should not think of the universe as described by a specific solution to the gravitational field equations; instead, it should be treated as a special physical system governed by a different mathematical description, rooted in the quantum description of spacetime. I will outline how this can possibly be done.