  In topological semimetals such as Weyl, Dirac, and nodal-line semimetals, the
band gap closes at points or along lines in k space which are not necessarily
located at high-symmetry positions in the Brillouin zone. Therefore, it is not
straightforward to find these topological semimetals by ab initio calculations
because the band structure is usually calculated only along high-symmetry
lines. In this paper, we review recent studies on topological semimetals by ab
initio calculations. We explain theoretical frameworks which can be used for
the search for topological semimetal materials, and some numerical methods used
in the ab initio calculations.
