The Burgers equation is a basic hydrodynamic model describing the evolution of the velocity field of sticky dust particles. When supplied with random forcing it turns into an infinite-dimensional random dynamical system that has been studied since late 1990's. The variational approach to Burgers equation allows to study the system by analyzing optimal paths in the random landscape generated by the random force potential. Therefore, this is essentially a random media problem. For a long time only compact cases of Burgers dynamics on the circle or a torus were understood well. In this talk I discuss the Burgers dynamics on the entire real line with no compactness or periodicity assumption. The main result is the description of the ergodic components and One Force One Solution principle on each component. Joint work with Eric Cator and Kostya Khanin.