Red dwarfs are one of the smallest and dimmest main-sequence stars. With the improvement of observation technology, a rich population of planets have been discovered around them, which exhibits distinct distribution characteristics from planets around Solar-like stars. Earth-like planets have a higher occurrence rate around red dwarfs, and the planetary systems are tightly compact. The closer habitable zone makes it easier to search for habitable planets. The distribution of the radius valley between super-Earths and sub-Neptunes also differs from that around solar-like stars. Moreover, the discovery of giant planets around these low-mass stars can be hard to explain by current leading theories of planet formation. As the mass of solid material in the protoplanetary disk decreases with decreasing stellar masses, the formation of giant planets remains challenging. The observations from telescopes such as Transiting Exoplanet Survey Satellite (TESS), James Webb, and Atacama Large Millimeter/submillimeter Array (ALMA), have provided invaluable insights and opportunities for the study of planetary formation. In this paper, we review the observations of different populations of planets and summarize the up-to-date understanding of planetary formation around red dwarfs.