Recently molecules involving one or more Rydberg excitations have attracted considerable attention due to their unusual properties. Besides the exaggerated characteristics of the Rydberg atom (Rydberg atoms are highly excited atoms with principal quantum numbers n ranging from about ten upwards to several hundred.), such as small binding energies, large size, long lifetime, and huge polarizability, they possess abundant vibrational energy levels, exotic adiabatic potentials, permanent electric dipole moments and sensitivity to external fields, which make them not only include the excellent properties of the Rydberg atom, but also have been widely used in quantum information storage, quantum simulation, and evenmedicine, which has strongly aroused the research interest of scholars at home and abroad. According to the different binding mechanisms, Rydberg atoms can generally form three types of Rydberg molecules. The first type of Rydberg molecules is formed by two Rydberg atoms that interact via long-range electrostatic multipole interactions, often referred to as Rydberg macrodimers. Another class of Rydberg molecules is a bound state between ground-state and Rydberg-excited atoms. Its binding mechanism is a result of attractive interaction induced by the low-energy scattering of a Rydberg electron from an atom with a negative scattering length, and is often described by the Fermi pseudopotential model. The third type of Rydberg molecules is formed through long-range electric-multipole interaction between the Rydberg atoms and pointlike positive ions. Similar to the Rydberg macrodimers, the adiabatic potential energy curves of Rydberg molecules arise from nonperturbative solutions of the atom-ion interaction Hamiltonian. In this paper, we review the theoretical and experimental research progress of diatomic Rydberg molecules in recent years, including the formation mechanisms of different types of Rydberg molecules, experimental observations, and the study of their spectral properties, which will provide references for researchers who are engaged in or will be engaged in Rydberg molecules, and provide a theoretical and experimental basis for further study of Rydberg molecules.