The effect of interactions on quantum particles is a long standing question, with important consequences for most realistic systems.  In one dimension interactions usually lead to a radically new type of physics, very different from the one we know for higher dimensional systems.
I will present the main concepts underlying this physics, known as Luttinger liquids, and show the various realizations of such systems that recent progress in material science, nanotechnology and cold atomic physics have provided.  I will discuss where the field is standing now, and what are today's challenges, such as going beyond the Luttinger liquid concept.