Spintronics and pseudospintronics in graphene and topological insulators are explored in this review. Both materials are described by massless Dirac equations, but differ in spin-orbit coupling strength. Graphene has weak spin-orbit coupling, making it a good spin-conserver, while topological insulators have strong spin-orbit coupling, making them good spin-generators. The review discusses spin relaxation mechanisms, spin-orbit coupling, and the role of pseudospin in graphene. It also covers the spin Hall effect, spin relaxation in graphene and topological insulators, and the potential for spintronics applications in these materials. The review highlights the unique properties of graphene and topological insulators, including their potential for spintronic devices and their ability to support long spin relaxation times. The review concludes that further research is needed to fully understand and exploit the spintronic properties of these materials.Spintronics and pseudospintronics in graphene and topological insulators are explored in this review. Both materials are described by massless Dirac equations, but differ in spin-orbit coupling strength. Graphene has weak spin-orbit coupling, making it a good spin-conserver, while topological insulators have strong spin-orbit coupling, making them good spin-generators. The review discusses spin relaxation mechanisms, spin-orbit coupling, and the role of pseudospin in graphene. It also covers the spin Hall effect, spin relaxation in graphene and topological insulators, and the potential for spintronics applications in these materials. The review highlights the unique properties of graphene and topological insulators, including their potential for spintronic devices and their ability to support long spin relaxation times. The review concludes that further research is needed to fully understand and exploit the spintronic properties of these materials.