Phase change materials used in thermal energy storage systems are critical for energy utilization. Organic phase change materials have received considerable attention both for applications and research due to their favorable properties, such as large latent heat, low cost, stability, nontoxicity, and corrosion resistance. Because of the inherently low thermal conductivity, there has been a lot of research on various combinations of organic phase change materials with high conductivity materials. Carbon nanotubes, graphene and porous carbon have excellent properties, such as ultrahigh surface area and high thermal conductivity, which have become the preferred materials for thermal properties enhancement. Benefit from the varied dimensional spaces for retaining materials, these carbon-based materials can act as excellent confinement for phase change materials to form shape stabilized, phase change tunable, and thermally enhanced phase change composites. In this paper, a review about recent advancement and challenges for organic phase change materials confined in different types of carbon-based materials is presented, associated with some relevant theories trying to understand the mechanism of heat transfer and phase change in micro/nano confinement. Some promising applications in thermal management and energy conversion that have great potential for more explorations are also introduced.