Overview: Optical coherence, as a fundamental resource in all areas of optical physics, plays a vital role in understanding interference, propagation, scattering, imaging, light-matter interactions, and other fundamental characteristics from classical to quantum optical wave fields. The theory of optical coherence is the most powerful tool to describe the statistical characters of random light beams (also named partially coherent beams). In the space-frequency domain, the spatial coherence property of a partially coherent light beam is characterized by a two-point spectral degree of coherence that is a normalized version of the cross-spectral density function. Nowadays, the degree of coherence has been viewed as a novel degree of freedom for the structured partially coherent light beams, which is akin to the deterministic properties, such as the amplitude, phase, and polarization of a fully coherent structured light beam. Due to the fundamental difference between the two-point degree of coherence of partially coherent light and the one-point deterministic features of fully coherent light, the partially coherent beams with customized spatial coherence have shown many unique properties and been found to be more advantageous in particular applications. By simply adjusting the spatial coherence width of the degree of coherence for a partially coherent beam can help reduce the turbulence-induced signal distortion in free-space optical communications and resist the speckle noise in optical imaging. Only recently, it has been found that not only the spatial coherence width but also the spatial coherence distribution of the degree of coherence can be customized, which has enabled a host of novel physical effects, including beam’s self-shaping, self-reconstruction, and self-focusing, and has aroused many important potential applications. In this paper, we review the fundamental theory and efficient experimental protocols for tailoring the spatial coherence structure of the degree of coherence for the partially coherent light beams. The differences and the advantages between the two strategies for producing the partially coherent beams with nonconventional spatial coherence structures are discussed. Meanwhile, we mainly focus on the applications of the spatial coherence structure engineering in coherence-based optical encryption, robust optical imaging, sub-Rayleigh imaging, robust far-field information transfer, and high-quality beam shaping. It is found that the spatial coherence structure engineering provides an efficient degree of freedom for the manipulation of structured light and paves the way for resisting the side effects induced by random fluctuations of complex media. We prospect that the spatial coherence engineering protocols can be extended to the temporal domain or even to the spatiotemporal domain and will find broader applications for light manipulations and light-matter interactions.Structured light has rich adjustable spatial degrees of freedom, including amplitude, phase, polarization, degree of coherence, etc. The modulation of these degrees of freedom has triggered a variety of novel physical effects and has found use in constructing new structured light beams and a large range of applications. Compared to the fully coherent light, partially coherent beams (PCBs) have advantages in resisting the speckle noise and the fluctuations of atmospheric turbulence. Recently, the PCBs with nonconventional coherence structures have been found to have important potential applications in atmospheric transmission, optical encryption and imaging, robust information transmission, and high-quality beam shaping. In this review, we summarize in detail the progress of the theoretical construction and experimental generation of PCBs with novel coherence structures. Meanwhile, we outline their robust propagation properties in complex media and important applications in optical encryption, imaging, robust information transfer, and beam shaping. It is found the modulation of spatial coherence structure of PCBs provides not only an efficient way to resist the random fluctuations of complex environments, but also a new degree of freedom to enrich the application scopes of structured light. Finally, the development trend and the further applications of the nonconventional coherence structure engineering are prospected.