The exploration of the critical point on the QCD (Quantum Chromodynamics) phase diagram is one of the most important goals of the beam energy scan program in relativistic heavy-ion collisions (RHIC-BES). Preliminary experimental measurement observed the non-monotonic behavior of net-proton fluctuations as a function of collision energy, which qualitatively agrees with the prediction of the static theoretical models and this hints the existence of the QCD critical point. The system created in heavy-ion collision is highly expanding system with which the dynamical effects dramatically modify the critical fluctuations near the QCD critical point. To confirm the existence of QCD critical point and study the phase structure of QCD system at finite temperature and finite density region, a series of dynamical models near the QCD critical point has been developed. This paper reviews the recent developments related to the exploration of the QCD critical point from experimental and theoretical viewpoints. In particular, we emphasize on the developments and challenges of the dynamical model near the QCD critical point and the first-order phase transition.