The quantum Spin Hall Insulator (QSHI) is a two-dimensional variant of a novel class of materials characterized by topological order, whose unique properties have recently triggered much interest and excitement in the condensed matter community. Most notably, the topological properties of these systems hold great promise in mitigating the difficult problem of decoherence in implementations of quantum computers. Although QSHI has been theoretically predicted in a few different materials, prior to the work presented in this thesis, only the HgTe/CdTe semiconductor system has shown direct evidence for the existence of this phase. Ideally insulating in the bulk, QSHI is characterized by one-dimensional channels at the sample perimeter, which have a helical property, with carrier spin tied to the carrier direction of motion, and protected from elastic back-scattering by time-reversal symmetry. In this thesis we present low temperature transport measurements, showing strong evidence for the existence of proposed helical edge channels in InAs/CaSb quantum wells, which thus emerge as an important alternate to HgTe/CdTe quantum wells in studies of two-dimensional topological insulators and superconductors. Surprisingly, edge modes persist in spite of comparable bulk conduction of non-trivial origin and show only weak dependence on magnetic field in mesoscopic devices. We elucidate that the seeming independence of edge on bulk transport comes due to the disparity in Fermi wave-vectors between the bulk and the edge, leading to a total internal reflection of the edge modes. Furthermore, low Schottky barrier of this material system and good interface to superconductors allows us to probe topological properties of helical channels in Andreev reflection measurements, opening a promising route towards the realization of topologically superconducting phases hosting exotic Majorana modes.