In this thesis, we will focus on a very general family of variational wave-functions, whose main peculiarity is that their descriptors/parameters are tailored according to simple linear algebraic relations. The computational power and success of these tools descends from arguments that were born within quantum information framework: entanglement [1]. Quantum entanglement is indeed a resource, but it is also a measure of internal correlations in multipartite systems. Once we characterized general entanglement properties of many-body ground states, then by controlling entanglement of a variational trial wavefunction we can exclusively address physical states, and disregard non-physical states, even before the simulation takes place. This is the central concept which Tensor Network architectures are based upon.
