Polyisobutylene is unique among elastomeric polymers in that while the glass transition temperature is low (-70 degrees C), segmental dynamics at temperatures above T-g are relatively slow due to steric constraints resulting from the molecular packing of methyl groups. We describe results from NMR experiments on solid polyisobutylene (PIB) and copolymers with p-methylstyrene (PIB-PMS) in which the dynamics of chain motion in PIB homopolymers and PIB-PMS copolymers are compared as a function of temperature. Our one-and two-dimensional solid-state H-1, C-13, and H-2 results clarify previously published reports on local vs correlated segmental dynamics for the PIB homopolymer, which differ by 4-5 orders of magnitude in their correlation times. Distinct differences in aromatic ring dynamics as a function of PMS concentration are also observed for PIB-PMS copolymers. While PMS dynamics are found to be sensitive to PMS concentration in the copolymer, PIB motions appear to be independent of the comonomer incorporation. These results may be understood based on the clustered or blocky incorporation of PMS comonomer segments in the polymer chain. This copolymer system represents a regime intermediate between random copolymers and phase-separated block polymers and may be considered a correlated random copolymer. Relaxation and 2D HETCOR experiments are used to define morphology for the PMS clusters in the copolymer, and the results are consistent with a 3 nm domain size for the clusters. Finally, the effects of curing on dynamics at the cross-link site for functionalized PIB-PMS copolymers are selectively examined using 2H wide-line experiments.