Title: "Rounding of 1st Order Quantum Phase Transitions in Low- Dimensional Systems with Quenched Disorder " Abstract: The addition of quenched disorder has a rounding effect on 1st order phase trans ition in systems of sufficiently low dimension (d=2, and up to � 4 in case of co ntinuous symmetry). The talk will focus on the recent extension to quantum pha se transition of a result that was previously proven for classical systems, and on a currently studied question concerning the nature of the disorder-dominated state in d=2 dimensions. (Work done in different collaborations.)