We discuss the effect of dissipation on quantum phase transitions. In particular we concentrate on the Superconductor to Insulator and Quantum-Hall to Insulator transitions. By invoking a phenomenological parameter α to describe the coupling of the system to a continuum of degrees of freedom representing the dissipative bath, we obtain new phase diagrams for the quantum Hall and superconductor-insulator problems. Our main result is that, in two-dimensions, the metallic phases observed in finite magnetic fields (possibly also strictly zero field) are adiabatically deformable from one to the other. This is plausible, as there is no broken symmetry which differentiates them.PACS numbers: 73.40.Hm Quantum phase transitions continue to attract intense theoretical and experimental interest; see, for example, [1][2][3][4][5]. Such transitions -where changing an external parameter in the Hamiltonian induces a transition from one quantum ground state to another, fundamentally different one -have been invoked to explain data from various experiments. Transitions that have been studied include the quantum-Hall liquid to insulator transition (QHIT), the quantum Hall liquid to quantum Hall liquid or "plateau" transition (QHPT), the metal to insulator transition (MIT) and the superconductor to insulator transition (SIT). Where the transition is continuous, quantum critical phenonema are expected to give rise to interesting, universal physics which it is common practice to analyze using a straightforward scaling theory, inherited from the classical theory of finite temperature phase transitions.Effects of dissipation, that is to say the coupling of the critical modes to a continuum of other "heat-bath" degrees of freedom, can fundamentally alter the character of the phases and of the transitions between them.[6-8] While in classical statistical mechanics, the dynamics and thermodynamics are independent of each other, in the quantum case they are intimately related. The dynamical relaxation processes that permit the system to reach equilibrium can be neglected in classical problems, but cannot be ignored in a quantum problem.Recently, compelling experimental evidence has accumulated of the existence of "metallic" phases, that is to say phases with finite dissipation in the zero temperature limit. There is as yet no microscopic understanding of these observations. We conjecture that a metallic phase is stabilized by strong-enough coupling to a dissipative heat-bath, which we characterize by a single phenomenological parameter, α, in a manner pioneered in early studies of macroscopic quantum tunneling and coherence [9]. Note that the present phenomenological approach is impervious to such important issues as whether the dissipation is intrinsic or extrinsic. For large enough α, quantum coherence can be suppressed even at zero temperature [10]. Thus, the conventional picture of quantum phase transitions is certainly dramatically altered, and As a paradigmatic example, consider the magnetic field driven SIT, for which the commo...