We present a dissipative pat tide dynamics simulation study on nanostructure formation of symmetric and asymmetric diblock copolymers confined between planar surfaces We consider symmetric and slightly asymmetric diblock copolymers that form lamellar nanostructures in the bulk, and highly asymmetric diblock copolymers that form cylindrical nanostructures in the bulk The formation of the diblock copolymer nanostructures confined between the planar surfaces is investigated and characterized by varying the separation width and the strength of the interaction between the surfaces and the diblock copolymers Both the slit width and the sui face Interaction strongly influence the phase diagram, especially for the asymmetric systems For the symmetric and slightly asymmetric diblock copolymer systems, the confinement primarily affects the orientation of the lamellar domains and only marginally influences the domain morphologies These systems form parallel lamellar phases with different number of lamellae, and perpendicular and mixed lamellar phases In a narrow portion of the phase diagram, these systems exhibit a parallel perforated lamellar phase, where further insight into the appearance of this phase is provided through free-energy calculations. The confined highly asymmetric diblock copolymer system shows, in addition to nanostructures with parallel and perpendicular cylinders, noncylindrical structures such as parallel lamellae and parallel perforated lamellae. The formation of the various confined nanostructures is further analyzed by calculating structural characteristics such as the mean glum e end-to-end distance of the diblock copolymers and the nematic order parameter