The family of carbon nanostructures includes a great number of forms with different properties derived from their reduced dimensionality. In particular, carbon nanotubes (CNTs) and graphene show special electronic, optical, mechanical and chemical properties that allow their potential application in new materials and devices. The real possibilities of pristine CNTs and graphene depend on their synthetic origin, which can be roughly classified into methods starting from graphite and chemical vapor deposition (CVD) processes. Applications of CNTs and graphene encompass electronics, energy devices, multifunctional composites, catalysis and sensors. Their reduced size and weight suggest potential uses in portable, wearable and mobile equipment with a high added value.