Publisher Summary This chapter reviews that the concept of aromaticity is one of the most general but also controversial constructs. The aim of this chapter is to review a critical analysis of various criteria of aromaticity, and the indices quantifying aromatic or antiaromatic character with an emphasis on the application to heterocyclic compounds. Designed as both an appropriate language for the analysis of specific features of structure, stability, and physical and chemical properties inherent in the conjugated cyclic molecular systems, and for their quantitative or semiquantitative evaluation, the concept of aromaticity has received special attention in the chemistry of heterocyclic compounds. It also emphasized that “it would be inconceivable to attempt to teach or practice heterocyclic chemistry without the use of the concept of aromaticity.” It has been long recognized that despite all its versatility and usefulness, the very idea of aromaticity lacks a secure physical basis. The aromaticity of cyclic systems is, in the first place, manifested in the stabilization (destabilization) effects of cyclic electron (bond), delocalization and non-additivity of the collective properties of a molecule.