Topological Materials (TMs) represent a new class of materials having unconventional electronic and transport properties controlled by band topology, with potential applications in future generations of quantum and spintronic devices. To date, several generations of TMs have been theoretically/computationally predicted and experimentally confirmed. In this talk, I will present our recent theoretical prediction and computational design of a few candidates of TMs, based on first-principles calculations and tight-binding model analyses. These include organic topological insulators, made of metalorganic frameworks, surface-based 2D Dirac and topological materials on semiconductor substrates, topological superconductors, and selected topics of strain engineering of TMs. Among them I will also show a couple of predictions that have already been confirmed by experiments. We envision that the emerging TMs will greatly broaden the scientific scope and technological impact of materials research.