Quantum field theory (QFT) is a unified conceptual and mathematical framework that encompasses a veritable cornucopia of physical phenomena, including phase transitions, condensed matter systems, elementary particle physics, and (via the holographic principle) quantum gravity. QFT has become the standard language of modern theoretical physics.Despite the fact that QFT is omnipresent in physics, we have virtually no tools to analyze from first principles many of the interesting systems that appear in nature. (For instance, Quantum Chromodynamics, non-Fermi liquids, and even boiling water.)Our main goal in this proposal is to develop new tools that would allow us to make progress on this fundamental problem. To this end, we will employ two strategies.First, we propose to study in detail systems that possess extra symmetries (and are hence simpler). For example, critical systems often admit the group of conformal transformations. Another example is given by theories with Bose-Fermi degeneracy (supersymmetric theories). We will explain how we think significant progress can be achieved in this area. Advances here will allow us to wield more analytic control over relatively simple QFTs and extract physical information from these models. Such information can be useful in many areas of physics and lead to new connections with mathematics. Second, we will study general properties of renormalization group flows. Renormalization group flows govern the dynamics of QFT and understanding their properties may lead to substantial developments. Very recent progress along these lines has already led to surprising new results about QFT and may have direct applications in several areas of physics. Much more can be achieved.These two strategies are complementary and interwoven.