A review is given of crystal structures and order/disorder phenomena in the fullerene solids C60, C60O and C70, and in the alkali metal intercalation compounds of C60. Recent results on orientational melting and quenched orientational disorder in the pristine solids are summarized, and the effect of small perturbations on the quasi-spherical molecular shape are described. The intercalation properties of C60 are discussed in the context of other host lattices such as graphite. The variety of orientational correlations in fullerenes and fullerides is rationalized in terms of competing contributions to the orientational potentials. Structural properties of alkali fullerides are correlated with electronic properties and superconductivity, and an updated binary phase diagram is described.