Although fullerenes and their compounds are very new and exhibit new phenomena, pressure has already been an important factor in the characterization and study of these materials. In order to illustrate this, we will review collaborative studies on: i) the effect of pressure on alkali and alkaline earth doped C60 superconductors, ii) the effect of pressure and pressure medium on the ordering temperature of C60, and iii) the role of pressure in the study of the feasibility of using C60 as "lattice sieves" for separation of gases.