  The KPZ fixed point is a scaling invariant Markov process which arises as the
universal scaling limit of a broad class of models of random interface growth
in one dimension, the one-dimensional KPZ universality class. In this survey we
review the construction of the KPZ fixed point and some of the history that led
to it, in particular through the exact solution of the totally asymmetric
simple exclusion process, a special solvable model in the class. We also
explain how the construction reveals the KPZ fixed point as a stochastic
integrable system, and how from this it follows that its finite dimensional
distributions satisfy a classical integrable dispersive PDE, the
Kadomtsev-Petviashvili (KP) equation.
