Two-dimensional (2D) electron systems (2DES) have enabled some of the most important developments in solid state physics (such as quantum Hall effects) and technologies (such as MOSFETs). In the last decade, new kinds of 2DESs with unusual properties have been realized in two-dimensional (2D) materials (such as graphene) as well as topological materials (such as topological insulators). In this talk, I will present some of our experimental explorations of these materials, which may enable us to engineer novel bandstructures, realize new regime of “topological” charge, spin and superconducting transport, create condensed matter analogs of Dirac/Weyl/Majorana fermions and other exotic particles, and develop potential device applications in areas such as spintronics, energy harvesting or even quantum computing.