This dissertation investigates the non-semisimple generalization of Turaev-Viro topological quantum field theories and their lattice model realizations. The goal is to find a categorical framework that generalizes the spherical fusion category theory for the semisimple case. Our approach is to start with the dual picture of categorical framework. By a theorem of Ostrik, every fusion category is the representation category of a certain quantum groupoid. So we work with non-semisimple quantum groupoids. The dissertation consists of three parts which consider different aspects of our goal. In the first part, we provide details of a proof for Kerler's conjecture about the structure of modular group representation on the centers of small quantum groups uqsl(2). In the second part, we study Kuperberg invariants and Hennings invariants for 3-manifolds which are non-semisimple generalizations of Turaev-Viro invariants and Reshetikhin-Turaev invariants. We show that for Lens spaces they satisfy a relation similar to that between Turaev-Viro invariants and Reshetikhin-Turaev invariants. In the third part, we establish a generalization of Kitaev models from unitary quantum groupoids. Then we show that based on a Kitaev-Kong quantum groupoid HC , the ground state manifold of the generalized model is canonical isomorphic to that of the Levin-Wen model based on the unitary fusion category C Therefore the generalized Kitaev models provide realizations of the target space of the Turaev-Viro TQFT based on C.