  We consider directed polymers in random environment in the critical dimension
$d = 2$, focusing on the intermediate disorder regime when the model undergoes
a phase transition. We prove that, at criticality, the diffusively rescaled
random field of partition functions has a unique scaling limit: a universal
process of random measures on $\mathbb{R}^2$ with logarithmic correlations,
which we call the *Critical 2d Stochastic Heat Flow*. It is the natural
candidate for the long sought solution of the critical 2d Stochastic Heat
Equation with multiplicative space-time white noise.
