The phase reconstruction technique plays an extremely important role in various fields, such as materials science, biomedicine, and astronomy. In different phase retrieval technologies and applications, different light sources are needed. The wavelength, coherence, and energy of a light source can all affect the final phase reconstruction. In previous studies, in terms of spatial coherence, a light source has often been considered completely coherent light. However, in the actual experiments, X-ray and electron beams both correspond to partially coherent light. Spatial coherence of fully coherent light propagated through a medium will reduce accordingly. Therefore, it is especially important to identify appropriate ways to realize correct reconstruction under partially coherent illumination. In this paper, we provide a review of the research background and progress in developing phase reconstruction methods under partially coherent illumination. Some common methods, such as mode decomposition, transport of intensity equation, self-reference holography, and focus variation, are introduced and their advantages and disadvantages are compared. Moreover, the application of the self-reference holography method to the measurement of the correlation function for a specially correlated partially coherent beam and the determination of the corresponding topological charge of a partially coherent vortex beam is also summarized.