This chapter contains sections titled: Introduction Free-radical Polymerization Coupling Reactions of Homopolymers Sequential Anionic Polymerization Sequential Group Transfer Polymerization Sequential Cationic Polymerization Non-radical Metal-catalyzed Polymerization Controlled Radical Polymerization Atom Transfer Radical Polymerization (ATRP) Nitroxide-mediated Polymerization (NMP) Reversible Addition Fragmentation Chain Transfer (the RAFT Process) Switching from One Polymerization Mechanism to Another Use of “Dual” Initiators in Concurrent Polymerization Mechanisms Chemical Modification of Pre-formed Block Copolymers Methods for the Synthesis of Block Copolymers with a Complex Architecture Conclusion References