  Tensor Network States are ans\"atze for the efficient description of quantum
many-body systems. Their success for one dimensional problems, together with
the fact that they do not suffer from the sign problem and can address the
simulation of real time evolution, have turned them into one of the most
promising techniques to study strongly correlated systems. In the realm of
Lattice Gauge Theories they can offer an alternative to standard lattice Monte
Carlo calculations, which are suited for static properties and regimes where no
sign problem appears. The application of Tensor Networks to this kind of
problems is a young but rapidly evolving research field. This paper reviews
some of the recent progress in this area, and how, using one dimensional models
as testbench, some fundamental milestones have been reached that may pave the
way to more ambitious goals.
