Francesco, Caravelli2012-08-232012-08-232012-08-232012-06-29http://hdl.handle.net/10012/6868In this thesis we review the status of an approach to Quantum Gravity through lattice toy models, Quantum Graphity. In particular, we describe the two toy models introduced in the literature and describe with a certain level of details the results obtained so far. We emphasize the connection between Quantum Graphity and emergent gravity, and the relation with Variable Speed of Light theories.enquantum graphityquantum gravityDoctoral ThesisPhysics