Topological insulators are characterized by boundary modes with very strong spin-momentum coupling. In proximity to a conventional superconductor, these modes are predicted to host topological superconductivity, an exotic state of matter that supports Majorana zero-modes . Localized Majorana modes obey non-Abelian exchange statistics, making them interesting building blocks for topological quantum computing. In this talk, I will describe our current efforts to realize topological superconductivity in nanostructures based on InAs/GaSb quantum wells, a two-dimensional topological insulator (2D TI). By electrostatically-gating the devices we observe superconducting transport in all three regimes of the 2D TI: bulk electrons, edge modes and bulk holes. We use superconducting quantum interference measurements as a sensitive method for determining the spatial distribution of the supercurrent in each regime. These measurements reveal a clear transition from bulk- to edge-dominated supercurrent under conditions of high bulk resistivity, which we associate with the 2D topological phase. These experiments establish InAs/GaSb as a promising platform for observing Majoranas modes and probing their exchange statistics.  J. Alicea, Rep. Prog. Phys. 75 076501 (2012).  V.S. Pribiag et al ., arXiv :1408.1701.