Many natural systems can be maintained in a stationary state through the exchange of matter, energy or information with their surroundings. These various currents break time-reversal invariance, generating a continuous increase of entropy in the universe. Such systems are out of equilibrium and can not be described by the Laws of Thermodynamics, or by using the classical principles of statistical physics, à la Gibbs-Boltzmann. In the last decades, however, important advances in our understanding of non-equilibrium processes have been achieved. Concepts of rares events, large deviations, fluctuations relations and macroscopic fluctuations provide a unified framework with the emergence of some universal features. The objective of this talk is to review these new ideas in non-equilibrium statistical physics and to illustrate them by examples inspired from soft-condensed matter.