<p indent=0mm>The synchrotron radiation light source based on electron storage ring is the most widely used high-performance X-ray source in the field of basic scientific research in the 20th century, and has undergone three generations of development. One important direction of the new generation light source, i.e., the fourth generation light source, is the so-called diffraction-limited storage ring (DLSR) light source. DLSR, with ultra-high average brightness, high repetition frequency, multi-user, high stability, complementary to the free electron laser (FEL), has a great development in recent decades. By adopting lattice design based on compact multi-bend achromats (MBAs), DLSR allows to achieve one or two orders of magnitude lower emittance approaching the diffraction limit of X-rays, and much higher brightness and coherence than available in the third generation light source, while inheriting the high brightness, multi-user and high stability advantages of existing ring light sources. In this paper, the progress made in the last few decades in physics design and optimization of the DLSR, especially on the ultralow-emittance lattice and injection schemes, will be overviewed. To achieve an ultralow emittance, lattice structures of standard MBA and hybrid MBA, and novel magnets of high-gradient quadrupole, antibend, longitudinal gradient dipole and complex bend, have been proposed. To obtain optimized beam dynamics in a DLSR, theoretical and numerical methods have been developed to date. Due to the fact that the nonlinearities are extremely high in a DLSR and the nonlinear dynamics is greatly coupled with the linear optics, the most effective and most commonly used way is global and stochastic optimization of the ring performance evaluated by numerical tracking. To deal with the challenges of injecting to a DLSR with small dynamic acceptance, different injection schemes, such as, pulsed multipole injection, on-axis swap-out injection and on-axis longitudinal injection, have been proposed. Collective effects, especially the intra beam scattering and the Touschek effects, become significant as emittance decreases, requiring methods of bunch lengthening and transverse feedback to ensure the stability of the particle motion at a high beam current. Besides, a few developing topics in DLSR physics will be discussed. Machine learning, the method of transferring disorder data into useful information, is an important branch of artificial intelligence, and has been used in accelerator control system and beam commissioning. This method would be very useful and helpful in the design and optimization, initial commissioning and daily operation of a DLSR. A rational combination of machine learning and multi-objective optimization algorithm, like multi-objective genetic algorithm and multi-objective particle swarm algorithm, can effectively improve the optimization performance, and has been successfully applied in nonlinear optimization of light sources. In addition, improving the performance of synchrotron radiation by combining the beam physics of DLSR and the principle of FEL is one developing research topic which might be able to provide base for further development of the DLSR. Combined with bypass and transverse gradient undulator, high gain FEL could be achieved in the storage ring. Besides, double ring light source, divided into two loops, the inner ring is DLSR, and the other is FEL with more long straight sections, was proposed to improve the utilization rate of the beams.