The recent successes of superconducting qubits and the demonstration of quantum supremacy over classical bits herald a new era for information processing. Yet, the field is still in its infancy and there exist viable alternative candidates that can also store quantum information. In this review, we will highlight ideas, attempts, and the experimental progress to address nuclear spins in graphene, a readily available Dirac semimetal that consists of a single layer of carbon atoms. Carbon isotopes with a nuclear spin are rare in natural graphene. However, it is possible to enrich the spin-bearing 13C isotopes to produce large-scale graphene sheets, which constitute the testbed to store, transport, and retrieve spin information, or to engineer nanostructures. Here, the hyperfine interaction between the electron spins and the nuclear spins serves as an experimental control knob and mediator to address nuclear polarization and nuclear spin coherence times through electrical measurements. The exploitation of nuclear spins in graphene is thus an alluring perspective. We will discuss methods to synthesize 13C graphene and show experimental approaches and challenges to exploit the relatively weak hyperfine interaction in two-dimensional 13C graphene devices. The ultimate purpose, i.e., the exploitation of nuclear spins in graphene for information processing, is not within reach, but its potential for future applications merits a revisit of the current state-of-the-art.