Block copolymer (BCP) self-assembly has attracted considerable attention for many decades because it can yield ordered structures in a wide range of morphologies, including spheres, cylinders, bicontinuous structures, lamellae, vesicles, and many other complex or hierarchical assemblies. These aggregates provide potential or practical applications in many fields. The present tutorial review introduces the primary principles of BCP self-assembly in bulk and in solution, by describing experiments, theories, accessible morphologies and morphological transitions, factors affecting the morphology, thermodynamics and kinetics, among others. As one specific example at a more advanced level, BCP vesicles (polymersomes) and their potential applications are discussed in some detail.