  We survey the connections between the six-vertex (square ice) model of 2d
statistical mechanics and random matrix theory. We highlight the same universal
probability distributions appearing on both sides, and also indicate related
open questions and conjectures. We present full proofs of two asymptotic
theorems for the six-vertex model: in the first one the Gaussian Unitary
Ensemble and GUE-corners process appear; the second one leads to the
Tracy-Widom distribution $F_2$. While both results are not new, we found
shorter transparent proofs for this text. On our way we introduce the key tools
in the study of the six-vertex model, including the Yang-Baxter equation and
the Izergin-Korepin formula.
