Non-Fermi liquids are systems in which the Fermi-liquid behaviour breaks down. The simplest example is a system of interacting fermions in one dimension, called the Luttinger liquid. Although Luttinger liquids are physically similar to Fermi liquids, the restriction to one dimension gives rise to several qualitative differences such as the absence of a quasiparticle peak in the momentum dependent spectral function, and the presence of spin-charge separation and of spin-density waves. One cannot ignore the existence of interactions in one dimension and has to describe the problem with a non-Fermi theory, where Luttinger liquid is one of them. At small finite spin temperatures in one dimension the ground state of the system is described by spin-incoherent Luttinger liquid (SILL).