The crystallization kinetics and resulting morphology of polyethylene (PE) in the presence of single wall carbon nanotubes (SWNT) are investigated in isotropic and aligned composites. A hot coagulation method was developed to incorporate SWNT loadings as high as 30 wt % with uniform distribution. Thermal analysis interpreted using the Avrami equation showed that the nanotubes provide nucleation sites to PE and accelerate the PE crystal growth rate while reducing the crystal dimensionality from spherulitic to disk-shaped. Nucleating on SWNT bundles significantly increases the shish density during melt fiber spinning, so that the PE microstructure is shish kebab with straight (not twisted) lamellae in I wt % SWNT-HDPE composite fibers. By comparing the orientations of SWNT and PE produced by various processing conditions, we show that SWNT bundles template the growth of PE crystals by imposing a growth direction perpendicular to the SWNT. This provides a new route toward controlling the SWNT-polymer inter-face and thereby the physical properties of nanocomposites.