In this talk, I am going to describe the recent progress in the study of Dirac fermions in condensed matter physics. Firstly, I’ll explain how Dirac fermions emerge as low energy excitations in periodic solids. In particular, I would like to emphasize the role of symmetry and dimensionality of the system on the conditions for an accidental band crossing. After that I’ll explain the topological properties and also the correlation induced critical phenomena in Weyl semimetals. Then I’ll introduce new Dirac-type fermions predicted in recent theoretical studies and propose a way to classify new Dirac excitations.