This review article emphasizes the current enlargements in the formation and properties of the various nanostructured aggregates resulting from the self-assembly of a variety of block copolymers (BCPs) in an aqueous solution. The development of the different polymerization techniques which produce polymers with a desired predetermined molecular weight and low polydispersity is investigated with regard to their technological and biomedical applications; in particular, their applications as vehicles for drug delivery systems are considered. The solution behavior of amphiphilic BCPs and double-hydrophilic block copolymers (DHBCs), with one or both blocks being responsive to any stimulus, is discussed. Polyion complex micelles (PICMs)/polymersomes obtained from the electrostatic interaction of a polyelectrolyte-neutral BCP with oppositely charged species are also detailed. Lastly, polymerization-induced self-assembly (PISA), which forms nanoscale micellar aggregates with controlled size/shape/surface functionality, and the crystallization-driven self-assembly of semicrystalline BCPs facilitated when one block of the BCP is crystallizable, are also revealed. The scalability of the copolymeric micelles in the drug delivery systems and pharmaceutical formations that are currently being used in clinical trials, research, or preclinical testing is emphasized as these micelles could be used in the future to create novel nanomedicines. The updated literature and the future perspectives of BCP self-assembly are considered.