The spectra of fullerenes C60 and C70, higher fullerenes C76, C78 and C84 and hydrogenated fullerenes (fulleranes) were studied in laboratory in the UV and in the visible spectral range and could be used for searching and recognizing these molecules in space. Furthermore, the radical cation spectra of all the mentioned fullerene series and also of a series of large and very large polycyclic aromatic hydrocarbons (PAHs) were generated in the laboratory and studied in the near infrared spectral range.