In 1757 Leonhard Euler discovered the equations governing the dynamical behavior of fluids. Since then the hydrodynamic method has been applied with great success in many areas of physics. In my lecture, I will discuss a much more recent addition, which is concerned with the hydrodynamic equations for integrable many-body systems. As a very exceptional feature they possess an extensive number of conserved fields. Prime examples are the repulsive delta Bose gas and the Toda lattice, either classical or quantum.