Many important models in integrable probability (e.g. the KPZ equation, solvable directed polymers, ASEP, stochastic six vertex model) can be embedded into Gibbsian line ensembles. This hidden probabilistic structure provides new tools to control the behavior and asymptotics of these systems. In my first talk, I will discuss the Airy line ensemble and its origins and properties. In my second talk, I will discuss the KPZ line ensemble and explain how this structure is used to probe the temporal correlation structure of the KPZ equation. In my final talk, I will zoom out and discuss the origins of this hidden structure. In my lectures I will try to work from first principles as much as possible. The TA sessions and problem sets will serve to reinforce and fill in details from the lectures. Additionally, there will be thematically relevant short talks delivered immediately after my lectures.