I will discuss our recent computational work aimed at predicting a variety of new classes of topological materials, including topological insulators (TIs), topological crystalline insulators, Weyl semi-metals, and quantum spin Hall insulators, all attracting intense current interest. [1-7] The special symmetry protected electronic states in topological materials hold the exciting promise of providing revolutionary new platforms for exploring fundamental science questions, and for the realization of multifunctional topological devices for thermoelectric, spintronics, information processing and other applications.  I. Zeljkovic et al., Nature Materials 14, 318 (2015);  J. He et al., Nature Materials 14, 577 (2015);  S.-Y. Xu et al., Science (2015);  M. Neupane et al., Physical Review Letters 114, 016403 (2015);  F.-C. Chuang, et al., Nano Letters 14, 2505 (2014);  Y. Zhang et al., Nature Nanotechnology 9, 111 (2014);  Y. He et al., Science 9, 608 (2014).