The dynamics of many-body systems, such as gases of particles or lattices of spins, often display, at large scales of space and time, a high degree of universality. Indeed, this dynamics is usually described by a few equations, those of hydrodynamics, representing
the flows of conserved currents such as those of particles and energy. This is because other "degrees of freedom" thermalise much more quickly, and the full dynamics projects onto that of conserved currents. In fact, surprisingly, even correlations between
local observables at large separations in time, and large-scale fluctuations, can be described by hydrodynamics. This is the object of various theories of hydrodynamic fluctuations, such as macroscopic fluctuation theory (for systems where diffusion dominates),
and its ballistic counterpart (for systems where persistent currents exist). I will introduce the main ideas behind such theories, restricting to systems in one dimension of space for simplicity. I will concentrate on perhaps the simplest and newest, ballistic
macroscopic fluctuation theory, taking simple examples such as the gas of classical hard rods (hard spheres, but in one dimension) - but many concepts are general.