The equation of state (EoS) of nuclear matter is a description of the macroscopic properties of nuclear matter under different thermodynamic conditions or external fields, which is critical for understanding the theory of the strong interaction—quantum chromodynamics (QCD), the nature of nuclei, the dynamics of heavy-ion collisions (HICs), the internal structure of compact stars, the merger of binary neutron stars, and other physical phenomena. Heavy-ion collisions (HICs) are the only method in laboratories to create nuclear matter with extreme conditions such as high temperatures and high densities. HICs at different energy levels offer the possibility to quantitatively study the properties of nuclear matter under diverse thermodynamic conditions. This paper mainly presents the current research status of the EoS of nuclear matter and introduces the fundamental observables in HICs that are sensitive to the EoS, as well as the typical experiments and results used to explore the EoS. The progress in studying the EoS containing strangeness is also described and its possible research directions in the future are also discussed. The status and progress of worldwide heavy-ion accelerators and experimental spectrometers in the high-baryon density region are introduced, including China’s large-scale scientific facilities, i.e HIRFL-CSR and HIAF, as well as the CEE experiment. Additionally, the opportunities and challenges for experimental research on the EoS of nuclear matter in China are discussed.