Acetylene, among the multitude of organic molecules discovered in space, plays a distinct role in the genesis of organic matter. Characterized by its unique balance of stability and reactivity, acetylene is the simplest unsaturated organic molecule known to have a triple bond. In addition to its inherent chemical properties, acetylene is one of the most prevalent organic molecules found across the Universe, spanning from the icy surfaces of planets and satellites and the cold interstellar medium with low temperatures to hot circumstellar envelopes where temperatures surge to several thousand kelvins. These factors collectively position acetylene as a crucial building block in the molecular diversification of organic molecules and solids present in space. This review comprehensively discusses the formation and expansion of carbon skeletons involving acetylene, ranging from the formation of simple molecules to the origination of the first aromatic ring and ultimately to the formation of nanosized carbon particles. Mechanisms pertinent to both hot environments, such as circumstellar envelopes, and cold environments, including molecular clouds and planetary atmospheres, are explored. In addition, this review contemplates the role of acetylene in the synthesis of prebiotic molecules. A distinct focus is accorded to the recent advancements and future prospects of research into catalytic processes involving acetylene molecules, which is a significant instrument in driving the evolution of carbon complexity in the Universe. The insights garnered from this review underscore the significance of acetylene in astrochemistry and potentially contribute to our understanding of the chemical evolution of the Universe.