We present recent progress in understanding the 2D stochastic heat equation, a singular stochastic PDE which lies beyond existing solution theories. We discuss the construction of a non-trivial renormalized solution exploiting the connection with a key model in statistical mechanics, the directed polymer in random environment. This leads to a novel universal object, called the critical 2D Stochastic Heat Flow. It provides a rare example of a non-Gaussian scaling limit at the phase transition point in the critical dimension. We review recent contributions that begin to reveal the structure and distinctive features of this process.