The combination of synchrotron Small- and Wide-Angle X-ray scattering (SAXS/WAXS), and thermal analysis was used to follow the evolution of crystalline morphology and crystallization kinetics in a series of melt-processed composites of poly(ethylene terephthalate) (PET) and multiwall carbon nanotubes (MWCNT). The as-extruded PET-MWCNT composites underwent both hot and cold isothermal crystallizations where a final oriented nanohybrid shish-kebab (NHSK) crystalline structure was observed. An oriented NHSK structure was seen to persist even after melting and recrystallization of the composites. From the scattering data, we propose a model whereby the oriented MWCNTs act as heterogeneous nucleation surfaces (shish) and the polymer chains wrap around them and the crystallites (kebabs) grow epitaxially outwards during crystallization. However, depending on crystallization temperature, unoriented crystallites also grow in the polymer matrix, resulting in a combination of a NHSK and lamellar morphology. In contrast, the neat PET homopolymer showed the sporadic nucleation of a classic unoriented lamellar structure under the same isothermal crystallization conditions. These results provide a valuable insight into the distinctive modification of the crystalline morphology of melt-processed polymer-MWCNT composites prior to any secondary processing, having a significant impact on the use of MWCNTs as fillers in the processing and modification of the physical and mechanical properties of engineering polymers. (C) 2017 Elsevier Ltd. All rights reserved.