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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 the 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. [ABSTRACT FROM AUTHOR]

M dwarf is not only one of the lowest mass stars in the main sequence stars, but also the most numerous stars in the Milky Way. Planets and habitable zones around M dwarfs are usually closer to their host stars than F, G, and K-type stars, so it is more convenient for us to discover new planets and observe habitable planets. On average, there are 2.5 low-mass planets orbiting around each M dwarf, which is about 3.5 times that of F, G, and K stars, while the occurrence rate of giant planets, which greatly depends on the metallicity of their host stars, is one order of magnitude lower than that of F, G, and K stars. Herein we apply a set of selection criteria to collect 401 planets around M dwarfs to investigate the property of planets. Statistical analysis shows that terrestrial planets, whose semi-major axes are less than 1 au, account for about 74% of the total number of planets. About twenty-eight Earth-sized planets orbit within the habitable zone of their stars, which means that there might be liquid water and atmosphere on planet surface. In addition, the average distance between planets and their host stars tends to increase with the masses of planets. According to the planetary mass-radius relationship, there is a turning point at 4 M ⊕ (mass of Earth). With few exceptions, most planets with mass < 4 M ⊕ may be composed of 65% silicate and 35% iron, otherwise the radius of planet grows rapidly with the increase of mass because of a substantial gaseous envelope. Approximately 60% planets around M dwarfs are in tightly packed planetary systems, whose orbital configuration is observed to be trapped into 3: 2, 5: 3, and 2: 1 mean motion resonances. To explain the formation of compact system, several scenarios have been proposed, for instance inside-out formation and pebble-driven planet formation, even though the initial position of planetary embryos remains ambiguous. The formation of giant planets around low-mass stars also challenges the existing planet formation theory. Fortunately, high precision and resolution observation of space and ground-based telescopes is unveiling the structure of protoplanetary disks gradually, which offers the crucial initial conditions of planet formation, as well as the observation of planetary atmospheric composition. [ABSTRACT FROM AUTHOR]