A general overview is given over fullerenes under pressure, with an emphasi
s on polymeric phases produced by treatment of C-60 and C-70 under high pre
ssure. The pressure-temperature phase diagrams of these materials are brief
ly reviewed. The discussion centers on recent advances regarding tho detail
s of the crystal structures and the electron structures and electronic tran
sport properties. in particular for the one- and two-dimensional phases of
C-60. Several polymerized phases of C-70 are also discussed.