In this talk, I will first review certain non-perturbative aspects of QCD, focusing on a surprisingly powerful yet simple probe of such dynamics, namely the spectral density of Euclidean Dirac eigenmodes. I will then present the results of thermal lattice QCD simulations showing very surprising infrared behavior of this probe at sufficiently high temperatures. Based on these findings, I will argue that in the corresponding new regime — the “IR phase” of QCD — thermal fluctuations act to restore scale invariance at long distances in a non-trivial interacting manner. The nature of IR phase can be understood when viewed as a part of larger IR regime in the parameter space of SU(3) gauge theories with fundamental quarks. This connection is very fruitful and requires the revision of conventional ideas about the nature of strong dynamics in the vicinity of conformal window. Among other things, it leads to the proposal that the physics of strongly interacting near-perfect fluid medium observed at RHIC and LHC is in fact that of IR phase, and is characterized by glueball excitations becoming  effectively massless in large volumes.