Over the past decade, the fourth-generation synchrotron light sources based on diffraction-limited storage rings (DLSRs) have been extensively designed and developed around the world. In China, two fourth-generation synchrotron light sources, the High Energy Photon Source and the Hefei Advanced Light Facility, are being or will be constructed. This paper will report the main issues and progresses in physics design and optimization of DLSRs, including lattice design and optimization, beam injection and collective effects, and will also introduce the current design and construction status of DLSR facilities around the world.