Results on theoretical work, astronomical observations and laboratory measurements of the new form of carbon known as fullerenes and their hydrogenated forms (fulleranes) are reviewed. These molecules can be responsible for diffuse interstellar bands, for the UV bump, a prominent feature in the extinction curves observed in many lines of sight of our Galaxy and other galaxies, and the anomalous microwave emission discovered in several regions of star formation, in molecular clouds and HII regions. Recent detections of fullerene C_{60} and C_{70} in various astrophysical contexts from reflection nebulae to planetary nebulae and protoplanetary disks reinforce the hypothesis that fullerenes and fulleranes are common in the interstellar medium and could contribute significantly to extinction. Another potential agent of anomalous microwave emission processes and interstellar extinction bands are polycyclic aromatic hydrocarbons (PAHs). Identification of the simplest PAHs, naphthalene and anthracene, in the interstellar medium is also discussed.