Self-assembly of amphiphilic block copolymers display a multiplicity of nanoscale periodic patterns proposed as a dominant tool for the 'bottom-up' fabrication of nanomaterials with different levels of ordering. The present review article focuses on the recent updates to the self-association of amphiphilic block copolymers in aqueous media into varied core-shell morphologies. We briefly describe the block copolymers, their types, microdomain formation in bulk and micellization in selective solvents. We also discuss the characteristic features of block copolymers nanoaggregates viz., polymer micelles (PMs) and polymersomes. Amphiphilic block copolymers (with a variety of hydrophobic blocks and hydrophilic blocks; often polyethylene oxide) self-assemble in water to micelles/niosomes similar to conventional nonionic surfactants with high drug loading capacity. Double hydrophilic block copolymers (DHBCs) made of neutral block-neutral block or neutral block-charged block can transform one block to become hydrophobic under the influence of a stimulus (physical/chemical/biological), and thus induced amphiphilicity and display self-assembly are discussed. Different kinds of polymer micelles (viz. shell and core-cross-linked, core-shell-corona, schizophrenic, crew cut, Janus) are presented in detail. Updates on polymerization-induced self-assembly (PISA) and crystallization-driven self-assembly (CDSA) are also provided. Polyion complexes (PICs) and polyion complex micelles (PICMs) are discussed. Applications of these block copolymeric micelles and polymersomes as nanocarriers in drug delivery systems are described.