Vortex beams have physical properties such as spiral wave-fronts, phase singularities, and orbital angular momentum, which have important applications in particle manipulation, quantum information, super-resolution imaging, optical communication and so on, and become the spotlight of optical researches. Owing to the rapid development of the optical coherence theory, the researchers have introduced the coherence as a new degree of freedom into the vortex beams and proposed the partially coherent vortex beams as an extension of coherent vortex beams. Such partially coherent vortex beams, compared with the fully coherent ones, have their unique physical meanings and optical properties. Particularly, some new peculiar effects (such as coherence singularities, beam shaping, polarization switches, and self-healing) emerge when the coherence and the topological charges of the partially coherent vortex beams are modulated. Here, an overview on the fundamental theory and the development history of the partially coherent vortex beams is presented. The theoretical models, the propagation characteristics, the experimental generations and measurements, as well as the applications are introduced with the combination of our recent research works.