Polymer nanocomposites have been an area of active research for the past 20 years. Of all potential fillers for polymer nanocomposites, carbon nanotubes (CNTs) are of particular interest due to their low mass density, high aspect ratio, and excellent mechanical, electrical, and thermal properties. In semicrystalline polymer CNT nanocomposites (PCNs), CNTs are viewed as nucleation agents that can affect polymer crystallization. However, it is challenging to quantify and compare results from different research groups, mainly due to the complexity of CNTs. Different chiralities, diameters, surface functional groups, surfactants used, and sample preparation processes can affect PCN crystallization. In this Perspective, we will focus on the structure, morphology, and related applications of semicrystalline PCNs. We will first present the introduction to semicrystalline PCNs followed by a brief discussion on transcrystallization and linear nucleation in polymers. The detailed interface structure and morphology are best revealed by using the solution crystallization approach; novel nanohybrid shish-kebab structures have been observed. We will then discuss a few case studies with the focus on bulk crystallization, followed by polymer crystal-enabled applications, flow-induced crystallization in PCNs, and future outlook of the field.