Strongly correlated quantum systems, which are at the heart of many open problems in condensed matter, quantum chemistry, or high-energy physics, are challenging to understand due to their intricate entanglement structure. Quantum information theory provides the right framework to characterize highly entangled states and has given rise to the class of Tensor Network States, which capture the entanglement structure of strongly correlated systems by building the global wavefunction from local tensors and provide an efficient description of their low-energy states.In this project, we will develop a framework for the systematic study of strongly correlated systems using exact wavefunctions based on Tensor Network States. It will give us the tools to construct controlled families of states by encoding the relevant structure of the system directly into the wavefunction, rather than a Hamiltonian, and to study their behavior. Since the tensor describing the wavefunction also gives rise to an associated Hamiltonian, this establishes a framework for building solvable models with the tensor as the new central object.The novelty of our approach lies in the fact that quantum information gives us the tools to systematically construct wavefunctions for general strongly correlated systems, while at the same time, encoding the structure of the problem directly into the wavefunction results in small families of states with a direct physical interpretation of the parameters, unlike for fully variational approaches.We will apply our framework to study the physics of a range of strongly correlated models, in particular frustrated fermionic and spin systems, in order to understand the possible physics they can exhibit. This will enhance our understanding of the physics of strongly correlated systems, and, together with numerical results, experimental findings, and quantum simulations, ultimately lead to new applications and materials based on strongly correlated matter.