Polymeric micelles can be designed and synthesized to bear polymeric blocks with different hydrophilicities; this triggers their self-assembly into micellar aggregates similar to those generated with traditional surfactants. The basic structure consists of a hydrophobic core, capable of containing guest substances, and a hydrophilic shell, which stabilizes the payload and protects it from external degradation or prevents its quick elimination from the body. The accumulation of block copolymer micelles (BCMs) in a target cell or tissue can be accomplished by two main mechanisms, passive and active targeting; this allows the payload release at the site of action when desired. Hence, in this general overview, we pay special attention to newly developed single-stimulus-and multistimuli-responsive delivery systems capable of disassembling and reassembling (in some cases) as a response to changes in their physicochemical properties. Also, special interest is also devoted to multifunctional BCMs incorporating multiple therapeutic agents and/or multiple imaging contrast agents, which can be considered the new generation (third generation) of drug-delivery systems, that is, nanotheranostic platforms. Finally, a summary of BCM-based drug-delivery systems currently under clinical trials is given.