It seems interesting to adopt the idea of dance in the context of the arrangement of molecular blocks in the building of molecular systems. Just as various dances can create various feelings, the nature and arrangement of molecular blocks in the generated molecular system can induce different properties. We consider obtaining such “dancing” systems in which the still little-known azulene moieties are involved. The dark blue nonbenzenoid aromatic azulene has one less axis of symmetry relative to the two axes of its isomer, i.e., the fully benzenoid naphthalene, acquiring valuable properties as a result that can be used successfully in technical applications. In a dancing system, the azulene moieties can be connected directly, or a more or less complex spacer can be inserted between them. Several azulene moieties can form a linear oligomer or a polymer and the involvement of azulene moieties in nonlinear molecules, such as crown ethers, calixarenes, azuliporphyrins, or azulenophane, is a relatively new and intensely studied topic. Some aspects are covered in this review, which are mainly related to obtaining the mentioned azulene compounds and less to their characterization or physico-chemical properties.