Graphene, a single two-dimensional sheet of carbon atoms with an arrangement mimicking the honeycomb hexagonal architecture, has captured immense interest of the scientific community since its isolation in 2004. Besides its extraordinarily high electrical conductivity and surface area, graphene shows a long spin lifetime and limited hyperfine interactions, which favors its potential exploitation in spintronic and biomedical applications, provided it can be made magnetic. However, pristine graphene is diamagnetic in nature due to solely sp2 hybridization. Thus, various attempts have been proposed to imprint magnetic features into graphene. The present review focuses on a systematic classification and physicochemical description of approaches leading to equip graphene with magnetic properties. These include introduction of point and line defects into graphene lattices, spatial confinement and edge engineering, doping of graphene lattice with foreign atoms, and sp3 functionalization. Each magnetism-imprinting strategy is discussed in detail including identification of roles of various internal and external parameters in the induced magnetic regimes, with assessment of their robustness. Moreover, emergence of magnetism in graphene analogues and related 2D materials such as transition metal dichalcogenides, metal halides, metal dinitrides, MXenes, hexagonal boron nitride, and other organic compounds is also reviewed. Since the magnetic features of graphene can be readily masked by the presence of magnetic residues from synthesis itself or sample handling, the issue of magnetic impurities and correct data interpretations is also addressed. Finally, current problems and challenges in magnetism of graphene and related 2D materials and future potential applications are also highlighted.