The directed landscape is a random `directed metric’ on the
spacetime plane that arises as the scaling limit of integrable models
of last passage percolation. It is expected to be the universal
scaling limit for all models in the KPZ universality class for random
growth. In this talk, I will describe its construction in terms of the
Airy line ensemble via an isometric property of the
Robinson-Schensted-Knuth correspondence, and discuss some surprising Brownian structures that arise from this construction.
Based on joint work with M. Nica, J. Ortmann, B. Virag, and L. Zhang.