Precise synthetic methods to prepare functional block copolymers with heteroatoms (nitrogen, oxygen, sulfur, phosphorous, halogen, etc.) have received much attention for the fabrication of practical nanomaterials. Specifically, well-defined materials containing nitrogen-based functional groups show unique electrical, optical, and amphiphilic properties. To synthesize these products, living anionic polymerization is the most powerful method. However, the disruption of undesirable reactions is considered to be a great challenge in the anionic polymerization of functional monomers with heteroatoms. To overcome these problems, facile methods such as polymerization at low temperature, careful choice of additives and initiators, and the introduction of protective groups can be used. In this review, recent advances in the anionic polymerization of vinyl monomers with triphenylamine, carbazole, and pyridine moieties in the side chains will be discussed. Also covered is the morphological control of these polymers to obtain well-defined block copolymers for practical applications such as organic memory devices and light emitting diodes.