Topological materials host various novel quantum phases of electrons which are characterized by band topology and topologically protected surface/edge states. Despite recent progress, intense world-wide research activity in search of new classes of topological materials is continuing unabated. This interest is driven by the need for materials with greater structural flexibility and tunability to enable viable applications in spintronics and quantum computing. We have used first-principles band theory computations to successfully predict many new classes of topologically interesting materials, including Bi2Se3 series, the ternary half-Heusler compounds, TlBiSe2 family, Li2AgSb-class, and GeBi2Te4 family as well as topological crystalline insulator (TCI) SnTe family and Weyl semimetals TaAs, SrSi2, (Mo,W)Te2, Ta3S2, and LaAlGe family. I will also highlight our recent work on unconventional chiral fermions in RhSi and several material candidates for new TCI.