Topological semimetal, known as a type of topological quantum materials without energy gap, has attracted lots of research interests due to its unique physical properties such as novel quasiparticles, giant magnetoresistance and large carrier mobility. Topological semimetal can be further classified into topological Dirac semimetal, topological Weyl semimetal, topological nodal-line semimetal and topological semimetals with " new fermions”. The high-resolution angle-resolved photoemission spectroscopy (ARPES) has emerged as a powerful experimental technique to directly visualize the electronic structure and identify the characteristic topological electronic states in topological semimetals. Here we would briefly introduce the ARPES technique and review some of the recent progress of ARPES study on the electronic structures of typical topological semimetals. We would focus mostly on the physics origin and ARPES signature of topological electronic structures and hope the readers would find it interesting and useful in the understanding of this material class which both is important in physics and has promising application potentials.