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In this paper we reexamine recent results obtained by our group on the crystallization of nanocomposites and linear and miktoarm star copolymers in order to obtain some general features of their crystallization properties. Different nanocomposites have been prepared where a close interaction between the polymer matrix and the nano-filler has been achieved: in situ polymerized high density polyethylene (HDPE) on carbon nanotubes (CNT); and polycaprolactone (PCL) and poly(ethylene oxide) (PEO) covalently bonded to carbon nanotubes. In all these nanocomposites a “super-nucleation” effect was detected where the CNTs perform a more efficient nucleating action than the self-nuclei of the polymer matrix. It is believed that such a super-nucleation effect stems from the fact that the polymer chains are tethered to the surface of the CNT and can easily form nuclei. For polystyrene (PS) and PCL block copolymers, miktoarm star copolymers (with two arms of PS and two arms of PCL) were found to display more compact morphologies for equivalent compositions than linear PS-b-PCL diblock copolymers. As a consequence, the crystallization of the PCL component always experienced much higher confinement in the miktoarm stars case than in the linear diblock copolymer case. The consequences of the topological confinement of the chains in block copolymers and nanocomposites on the crystallization were the same even though the origin of the effect is different in each case. For nanocomposites a competition between super-nucleation and confinement was detected and the behavior was dominated by one or the other depending on the nano-filler content. At low contents the super-nucleation effect dominates. In both cases, the confinement increases as the nano-filler content increases or the second block content increases (in this case a non-crystallizable block such as PS). The consequences of confinement are: a reduction of both crystallization and melting temperatures, a strong reduction of the crystallinity degree, an increase in the supercooling needed for isothermal crystallization, a depression of the overall crystallization rate and a decrease in the Avrami index until values of one or lower are achieved indicating a nucleation control on the overall crystallization kinetics.