  Motivated by the recent exact solution of the {\it stationary-state}
Kardar-Parisi-Zhang (KPZ) statistics by Imamura & Sasamoto (Phys. Rev. Lett.
{\bf 108}, 190603 (2012)), as well as a precursor experimental signature
unearthed by Takeuchi (Phys. Rev. Lett. {\bf 110}, 210604 (2013)), we establish
here the universality of these phenomena, examining scaling behaviors of
directed polymers in a random medium, the stochastic heat equation with
multiplicative noise, and kinetically roughened KPZ growth models. We emphasize
the value of cross KPZ-Class universalities, revealing crossover effects of
experimental relevance. Finally, we illustrate the great utility of KPZ scaling
theory by an optimized numerical analysis of the Ulam problem of random
permutations.
