Two-dimensional (2D) magnetism in van der Waals (vdW) atomic crystals and moiré superlattices has become a major topic in condensed matter physics and materials science since its first experimental discovery in 2016–2017. It serves as a powerful platform for studying phase transitions and exploring new matter phases, and offers new opportunities for applications in microelectronics, spintronics, magnonics, and optomagnetics. Despite rapid developments, further research is needed to achieve the goal of routinely implementing 2D magnets as quantum electronic components. This review covers basic concepts, historical efforts, and a comprehensive review of vdW-based 2D magnetism, concluding with potential future research directions. 2D magnetism concerns magnetic moment arrangements and their collective magnetic excitations in atomically thin materials. Theoretical studies date back to the 1940s–1970s, with experimental investigations beginning in quasi-2D bulk materials, then in magnetic elemental thin films, and later in defected graphene films. The field blossomed in vdW magnetic atomic crystals and twisted moiré superlattices after 2016–2017. Theoretical models include the Ising, XY, and Heisenberg spin Hamiltonians, which describe different spin interactions. The Ising model, with spin dimension n=1, predicts long-range magnetic order at finite temperatures. The XY model, with n=2, exhibits quasi-long-range order. The Heisenberg model, with n=3, shows no long-range order due to enhanced spin fluctuations. The Dzyaloshinskii-Moriya (DM) interaction and Kitaev interaction are also important, influencing magnetic order and spin wave properties. Historically, experimental efforts in 2D magnetism began in the 1960s with quasi-2D bulk magnets, expanded to magnetic elemental thin films in the 1980s, and later to defected graphene monolayers in the 2000s. The late 2010s saw the discovery of intrinsic 2D vdW magnetic atomic crystals and moiré superlattices, leading to rapid growth in the field. The vdW materials platform for 2D magnetism includes vdW magnetic atomic crystals and twisted moiré superlattices. These systems exhibit unique magnetic properties due to their low dimensionality and strong spin interactions. Examples include 3d transition metal compounds, 4d transition metal halides, and 5d transition metal-based materials. These materials show diverse magnetic behaviors, including ferromagnetism, antiferromagnetism, and exotic spin states like skyrmions and quantum spin liquids. The field of 2D vdW magnetism is rapidly expanding, offering new insights into phase transitions and potential applications in spintronics and quantum electronics. Future research directionsTwo-dimensional (2D) magnetism in van der Waals (vdW) atomic crystals and moiré superlattices has become a major topic in condensed matter physics and materials science since its first experimental discovery in 2016–2017. It serves as a powerful platform for studying phase transitions and exploring new matter phases, and offers new opportunities for applications in microelectronics, spintronics, magnonics, and optomagnetics. Despite rapid developments, further research is needed to achieve the goal of routinely implementing 2D magnets as quantum electronic components. This review covers basic concepts, historical efforts, and a comprehensive review of vdW-based 2D magnetism, concluding with potential future research directions. 2D magnetism concerns magnetic moment arrangements and their collective magnetic excitations in atomically thin materials. Theoretical studies date back to the 1940s–1970s, with experimental investigations beginning in quasi-2D bulk materials, then in magnetic elemental thin films, and later in defected graphene films. The field blossomed in vdW magnetic atomic crystals and twisted moiré superlattices after 2016–2017. Theoretical models include the Ising, XY, and Heisenberg spin Hamiltonians, which describe different spin interactions. The Ising model, with spin dimension n=1, predicts long-range magnetic order at finite temperatures. The XY model, with n=2, exhibits quasi-long-range order. The Heisenberg model, with n=3, shows no long-range order due to enhanced spin fluctuations. The Dzyaloshinskii-Moriya (DM) interaction and Kitaev interaction are also important, influencing magnetic order and spin wave properties. Historically, experimental efforts in 2D magnetism began in the 1960s with quasi-2D bulk magnets, expanded to magnetic elemental thin films in the 1980s, and later to defected graphene monolayers in the 2000s. The late 2010s saw the discovery of intrinsic 2D vdW magnetic atomic crystals and moiré superlattices, leading to rapid growth in the field. The vdW materials platform for 2D magnetism includes vdW magnetic atomic crystals and twisted moiré superlattices. These systems exhibit unique magnetic properties due to their low dimensionality and strong spin interactions. Examples include 3d transition metal compounds, 4d transition metal halides, and 5d transition metal-based materials. These materials show diverse magnetic behaviors, including ferromagnetism, antiferromagnetism, and exotic spin states like skyrmions and quantum spin liquids. The field of 2D vdW magnetism is rapidly expanding, offering new insights into phase transitions and potential applications in spintronics and quantum electronics. Future research directions