This article reviews the emergence of magnetism in graphene materials and nanostructures, highlighting the unique opportunities they offer for future technological applications such as spintronics. The review covers zero-dimensional graphene nanofragments, one-dimensional graphene nanoribbons, and defect-induced magnetism in graphene and graphite. Computational examples based on simple model Hamiltonians illustrate the physical mechanisms behind the emergence of magnetism. The article also discusses spin transport properties, proposed designs of graphene-based spintronic devices, magnetic ordering at finite temperatures, and recent experimental achievements. The review emphasizes the potential of light-element-based magnetism, particularly in carbon-based materials, and the importance of graphene's unique electronic structure in enabling novel physical phenomena. The discussion includes the application of counting rules to predict the number of zero-energy states and the total spin of graphene systems, as well as the role of edge magnetism in graphene nanoribbons. The article concludes with a discussion on the practical implications of these findings for spintronic devices and the challenges and opportunities in controlling magnetic properties in graphene nanostructures.This article reviews the emergence of magnetism in graphene materials and nanostructures, highlighting the unique opportunities they offer for future technological applications such as spintronics. The review covers zero-dimensional graphene nanofragments, one-dimensional graphene nanoribbons, and defect-induced magnetism in graphene and graphite. Computational examples based on simple model Hamiltonians illustrate the physical mechanisms behind the emergence of magnetism. The article also discusses spin transport properties, proposed designs of graphene-based spintronic devices, magnetic ordering at finite temperatures, and recent experimental achievements. The review emphasizes the potential of light-element-based magnetism, particularly in carbon-based materials, and the importance of graphene's unique electronic structure in enabling novel physical phenomena. The discussion includes the application of counting rules to predict the number of zero-energy states and the total spin of graphene systems, as well as the role of edge magnetism in graphene nanoribbons. The article concludes with a discussion on the practical implications of these findings for spintronic devices and the challenges and opportunities in controlling magnetic properties in graphene nanostructures.