The quantum chromodynamics (QCD) phase diagram is of great interest to researchers in the field of high energy nuclear physics. We review the present research status of several aspects of this topic. This review includes the search for the phase transition mechanism resulting in high-order baryon number fluctuations, how chiral imbalance, finite volume, and under rotations affect the QCD diagram, and the applications of the equation of states of dense QCD matter in the study of compact stars. The Nambu-Jona-Lasinio model and Dyson-Schwinger equations approach are the most commonly used methods described in this review. It is found that the theoretical results of high-order baryon number fluctuations are in good agreement with the experimental data. The chiral imbalance, finite volume, and rotation of quark-gluon plasma (QGP) have a quantitative impact on the chiral condensate and the QCD phase structure. In the study of compact stars, the theoretical results from equation of states of dense QCD matter agree well with pulsar observations. Further research will be required to form a complete understanding of the QCD phase diagram, particularly given the abundance of QGP.