Selberg’s celebrated central limit theorem shows that the logarithm of the zeta function at a typical point on the critical line behaves like a complex, centered Gaussian random variable with variance $\log\log T$. This talk will present recent results showing that the Gaussian decay persists in the large deviation regime, at a level on the order of the variance, improving on the best known bounds in that range. We also present various applications, including on the maximum of the zeta function in short intervals. Whilst the results are number theoretic, the tools used are predominantly probabilistic in nature. This work is joint with Louis-Pierre Arguin.