While one of the most promising applications of carbon nanotubes (CNTs) is to enhance polymer orientation and crystallization to achieve advanced carbon fibers, the successful realization of this goal has been hindered by the insufficient atomistic understanding of polymer-CNT interfaces. Herein, polyacrylonitrile (PAN)-CNT hybrid structures are theoretically studied as a representative example of polymer-CNT composites. Based on density functional theory calculations, it is first found that the relative orientation of polar PAN nitrile groups with respect to the CNT surface is the key factor that determines the PAN-CNT interface energetics and the lying-down PAN configurations are much more preferable than their standing-up counterparts. The CNT curvature is identified as another important factor, giving the largest binding energy in the zero-curvature graphene limit. Charge transfer analysis explains the unique tendency of linear PAN alignments on the CNT surface and the possibility of ordered PAN-PAN assembly. Next, performing large-scale molecular dynamics simulations, it is shown that the desirable linear PAN-CNT alignment can be achieved even for relatively large initial misorientations and further demonstrate that graphene nanoribbons are a promising carbon nano-reinforcement candidate. The microscopic understanding accumulated in this study will provide design guidelines for the development of next-generation carbon nanofibers.