  In recent years, three-dimensional topological insulators (3DTI) as a novel
state of quantum matter have become a hot topic in the fields of condensed
matter physics and materials sciences. To fulfill many spectacularly novel
quantum phenomena predicted in 3DTI, real host materials are of crucial
importance. In this review paper, we first introduce general methods of
searching for new 3DTI based on the density-functional theory. Then, we review
the recent progress on materials realization of 3DTI including simple elements,
binary compounds, ternary compounds, and quaternary compounds. In these
potential host materials, some of them have already been confirmed by
experiments while the others are not yet. The 3DTI discussed here does not
contain the materials with strong electron-electron correlation. Lastly, we
give a brief summary and some outlooks in further studies.
