Hybridizing nanocarbons, such as carbon nanotubes (CNTs) or graphene, with an active material is a powerful strategy towards designing next-generation functional materials for environmental and sustainable energy applications. While research on nanocomposites, created by dispersing the nanocarbon into polymer or ceramic matrices, began almost immediately after the popularization of CNTs and graphene in 1991 and 2004, respectively, nanocarbon hybrids are a relatively recent addition to the family of composite materials. In contrast to nanocomposites, which typically combine the intrinsic properties of both compounds, nanocarbon hybrids additionally provide access to both a large surface area required for gas/liquid-solid interactions and an extended interface, through which charge and energy transfer processes create synergistic effects that result in unique properties and superior performance. This progress report looks at the history of research on nanocarbons (fullerenes, CNTs and graphene) and their composites and hybrids, presents the origin of synergistic effects, reviews the most intriguing results on nanocarbon hybrid performance in heterogeneous catalysis, electrocatalysis, photocatalysis, batteries, supercapacitors, photovoltaics and sensors, and discusses remaining challenges and future research directions.