  Quantum simulation is a powerful tool to study a variety of problems in
physics, ranging from high-energy physics to condensed-matter physics. In this
article, we review the recent theoretical and experimental progress in quantum
simulation of Dirac equation with tunable parameters by using ultracold neutral
atoms trapped in optical lattices or subject to light-induced synthetic gauge
fields. The effective theories for the quasiparticles become relativistic under
certain conditions in these systems, making them ideal platforms for studying
the exotic relativistic effects. We focus on the realization of one, two, and
three dimensional Dirac equations as well as the detection of some relativistic
effects, including particularly the well-known Zitterbewegung effect and Klein
tunneling. The realization of quantum anomalous Hall effects is also briefly
discussed.
