Abstract: In this talk I discuss phase-field models of dynamic brittle fracture, based on a suitable adaptation of Griffith's criterion. In these models, which rely on the Ambrosio-Tortorelli approximation, the (d-1)-dimensional set that represents the crack is replaced by a function v, taking values in [0,1], called phase-field, which takes a value near 0 in a small neighborhood of the crack set, and a value near 1 far from it. By using a time discretization scheme, I prove existence of a solution for a particular phase-field model which avoids viscoelastic terms on the displacement, and takes into account dissipative effects due to the crack tips speed. Finally, under some conditions on this dissipative term, I show that the evolution satisfies an energy-dissipation balance, according to Griffith's criterion.