Crystallization-induced phase separation and segmental relaxations in poly(vinylidene fluoride)/poly(methyl methacrylate) (PVDF/PMMA) blends was systematically investigated by melt-rheology and broadband dielectric spectroscopy in the presence of multiwall carbon nanotubes (MWNTs). Different functionalized MWNTs (amine, -NH2; acid, -COOH) were incorporated in the blends by melt-mixing above the melting temperature of PVDF, where the blends are miscible, and the crystallization induced phase separation was probed in situ by shear rheology. Interestingly, only -NH2 functionalized MWNTs (a-MWNTs) aided in the formation of beta-phase (trans-trans) crystals in PVDF, whereas both the neat blends and the blends with -COOH functionalized MWNTs (c-MWNTs) showed only alpha-phase (trans-gauche-trans-gauche') crystals as inferred from wide-angle X-ray diffraction (WXRD) and Fourier transform infrared (FTIR). Furthermore, blends with only a-MWNTs facilitated in heterogeneous nucleation in the blends manifesting in an increase in the calorimetric crystallization temperature and hence, augmented the theologically determined crystallintion induced phase separation temperature. The dielectric relaxations associated with the crystalline phase of PVDF (alpha(c)) was completely absent in the blends with a-MWNTs in contrast to neat blends and the blends with c-MWNTs in the dielectric loss spectra. The relaxations in the blends investigated here appeared to follow Havriliak-Negami (HN) empirical equations, and, more interestingly, the dynamic heterogeneity in the system could be mapped by an extra relaxation at higher frequency at the crystallization-induced phase separation temperature. The mean relaxation time (tau(HN)) was evaluated and observed to be delayed in the presence of MWNTs in the blends, more prominently in the case of blends with a-MWNTs. The latter also showed a significant increase in the dielectric relaxation strength (Delta epsilon). Electron microscopy and selective etching was used to confirm the localization of MWNTs in the amorphous phases of the interspherulitic regions as observed from scanning electron microscopy (SEM). The evolved crystalline morphology, during crystallization-induced phase separation, was observed to have a strong influence on the charge transport processes in the blends. These observations were further supported by the specific interactions (like dipole induced dipole interaction) between a-MWNTs and PVDF, as inferred from FTIR, and the differences in the crystalline morphology as observed from WXRD and polarized optical microscopy (POM).