A broad overview of the polymer chemistry based on carbon-carbon triple bonds and the structures and properties of the acetylenic polymers, was investigated. Acetylenic molecules have been developed into a group of versatile monomers with multifaceted reactivities and rich polymerization behaviors. They have emerged as a new family of advanced materials with novel structures and unique functionalities. The utilization of rich chemistry of the acetylenic monomers has enabled the design and synthesis of a great diversity of acetylenic macromolecules with desired structures, under the condition that monomer structures and catalyst systems are matched. The topological structures of the polymers can be linear or nonlinear, mainly determined by the selections of the monomeric building blocks and the choices of the construction strategies or synthetic routes. The structural tunability by the internal perturbations and external stimuli have enabled the researchers to develop a large variety of acetylenic polymers with an array of advanced functional properties.