A Chineese research group found recently two new phases in our previously prepared fullerene-cubane system after a high-pressure treatment: (i) a crystalline material of amorphous constituents; and (ii) an extended amorphous solid, harder than diamond. Phase (i) has been addressed as a new type of partially disordered solids, but its microscopic structure has not been specified. The new materials complete the rich family of fullerene-cubane materials consisting of such exotic phases as recognition controlled cocrystals with rotor-stator dynamics, rotor-in-rotor materials and interpenetrating networks of percolating copolymers. In the first part of the talk I outline the general structural characteristics of fullerenes, which are responsible for the great variety of their solid state reactions and the propensity for the formation of disordered solid derivatives. Then I discuss the polymers and cocrystals of fullerenes stressing the role of static and dynamic disorder. I detail the rotor-stator properties and the thermal copolymerization of various fullerene-cubane cocrystals. Finally I suggest a preliminary molecular model for the structure of the recently found phase (i).