In this thesis, several cases of non-equilibrium phenomena and quantum phase transitions in strongly correlated electron systems are analyzed.The unconventional critical behavior near magnetic quantum phase transitions in various heavy-fermion metals has triggered proposals on the breakdown of the Kondo effect at the critical point. In part I, we investigate, within one specific scenario, the fate of such a zero-temperature transition upon coupling of the electronic to lattice degrees of freedom. We study a Kondo-Heisenberg model with volume-dependent Kondo coupling - this model displays both Kondo volume collapse and Kondo-breakdown transitions. Within a large N treatment, we find that the Kondo breakdown transition remains of second order except for very soft lattices. Finally, we relate our findings to current heavy-fermion experiments. Using non-equilibrium Green's functions, we derive transport equations for the degrees of freedom participating in the quantum critical region of the Kondo breakdown transition. We discuss conditions under which the transport of electrical charge is described by the independent motion of conduction electrons and auxiliary bosons. Under these conditions, we derive a semiclassical transport equation for the bosons and quantitatively discuss the electrical conductivity of the whole system.