The topological insulator (TI) is a newly discovered phase in condensed matter systems. The TI is featured by a bulk energy gap originating from spin-orbit coupling and time-reversal symmetry protected gapless surface states, which is distinct from the conventional band insulator. Recently the topological classification has been extended beyond insulators; part of the research interest in topological phenomena in condensed matter has been moved from insulator to semimetals, leading to a new topological phase, topological semimetals (TSMs). Topological semimetal is the three-dimensional analog of graphene in which the bulk band shows a linear dispersion relation from the nodal point in all three momentum directions, or displays one-dimensional nodal-loop in Brillouin zone. In this talk, I will briefly introduce the key concepts of topology in condensed matter physics and then show our recent predications on TSMs, Weyl semimetals and nodal-line semimetals. We will focus on their electronic structures and discuss the fundamental physics.