Initial conditions for the cosmological evolution of the universe remain one of the biggest unresolved puzzles in nature. A large set of ideas pertaining to this puzzle are based on the theory of inflation — a period of an exponentially fast expansion of space. Despite its conceptual success and a number of experimental confirmations, our understanding of inflation is far from complete. The issues include a lack of an efficient formalism for performing basic perturbative calculations, appearance of infrared divergences, as well as more foundational ones, like an ambiguity in the initial conditions for inflation itself. In this talk I will review these problems and report on our progress in rectifying them. In particular, I will explain a novel set of tools for computing the inflationary correlation functions and demonstrate their properties related to fundamental principles like unitarity and causality. In the remaining part of the talk, I will touch upon non-perturbative gravitational effects that may prove to be important in a consistent description of the state of the early universe.