The Dirac, Weyl and Nodal-line states have attracted great research interest in condensed matter physics and material science. In this talk, I will introduce two works on topological semimetals. (1) Based on first-principles calculations and symmetry analysis, we report that Ag2S with P212121 symmetry is a topological Dirac semimetal in the absence of spin-orbit coupling (SOC). Every Dirac points are composed of two Weyl points with the same chirality overlapping in the momentum space. After taking the SOC into consideration, each Dirac point is split into two Weyl points and lead to long Fermi-arcs on material surface. (2) We introduce a scheme to realize topological nodal states with a three-dimensional periodic inductor-capacitor (LC) circuit lattice, where the topological nodal line state and Weyl state can be achieved by tuning the parameters of inductors and capacitors. The key characters of the topological states, such as the drumhead-like surface bands for nodal line state and the Fermi arc-like surface bands for Weyl state, are found in these systems.