The article provides a comprehensive review of two-dimensional (2D) magnetism in van der Waals (vdW) materials, highlighting its emergence as a significant field of research in condensed matter physics and materials science. The review begins with the basic concepts and properties of 2D magnetism, including theoretical models such as the Ising, XY, and Heisenberg models, and their implications for magnetic order and disorder. It then delves into the historical development of experimental efforts, from quasi-2D bulk materials in the 1960s to the discovery of 2D vdW magnets in the late 2010s. The article discusses the two primary families of 2D vdW magnets: atomic crystals with intrinsic magnetic moments and twisted moiré superlattices with flat bands. For atomic crystals, the focus is on 3d transition metal compounds, which have gained significant attention due to their diverse magnetic properties, including ferromagnetic and antiferromagnetic phases. The review also explores the crystal structures and magnetic behaviors of these compounds, such as CrXTe$_3$, MPX$_3$, and MXY. For twisted moiré superlattices, the article highlights the emergence of noncollinear spin textures, skyrmion lattices, and moiré magnons, driven by the competition between interlayer and intralayer exchange couplings. The review also discusses the correlation-induced 2D magnetism in twisted graphene and transition metal dichalcogenides (TMDCs), which arise from strong electronic correlations. Finally, the article concludes with a discussion on potential future research directions, emphasizing the rapid growth and novel applications of 2D vdW magnets in microelectronics, spintronics, magnonics, and optomagnetics. The review underscores the importance of further efforts to achieve routine implementation of 2D magnets as quantum electronic components.The article provides a comprehensive review of two-dimensional (2D) magnetism in van der Waals (vdW) materials, highlighting its emergence as a significant field of research in condensed matter physics and materials science. The review begins with the basic concepts and properties of 2D magnetism, including theoretical models such as the Ising, XY, and Heisenberg models, and their implications for magnetic order and disorder. It then delves into the historical development of experimental efforts, from quasi-2D bulk materials in the 1960s to the discovery of 2D vdW magnets in the late 2010s. The article discusses the two primary families of 2D vdW magnets: atomic crystals with intrinsic magnetic moments and twisted moiré superlattices with flat bands. For atomic crystals, the focus is on 3d transition metal compounds, which have gained significant attention due to their diverse magnetic properties, including ferromagnetic and antiferromagnetic phases. The review also explores the crystal structures and magnetic behaviors of these compounds, such as CrXTe$_3$, MPX$_3$, and MXY. For twisted moiré superlattices, the article highlights the emergence of noncollinear spin textures, skyrmion lattices, and moiré magnons, driven by the competition between interlayer and intralayer exchange couplings. The review also discusses the correlation-induced 2D magnetism in twisted graphene and transition metal dichalcogenides (TMDCs), which arise from strong electronic correlations. Finally, the article concludes with a discussion on potential future research directions, emphasizing the rapid growth and novel applications of 2D vdW magnets in microelectronics, spintronics, magnonics, and optomagnetics. The review underscores the importance of further efforts to achieve routine implementation of 2D magnets as quantum electronic components.