We present and discuss carbon-rich compounds of astrochemical interest such as polyynes, acetylenic carbon chains and the related derivative known as monocyanopolyynes and dicyanopolyynes. Fullerenes are now known to be abundant in space, while fulleranes - the hydrogenated fullerenes - and other carbon-rich compounds such as very large polycyclic aromatic hydrocarbons (PAHs) and heavy petroleum fractions are suspected to be present in space. We review the synthesis, the infrared spectra as well as the electronic absorption spectra of these four classes of carbon-rich molecules. The existence or possible existence in space of the latter molecules is reported and discussed.