For the production of materials, the generation and storage of clean energy, as well as numerous other crucial industrial processes, metals and metal oxides are frequently used as catalysts. Metal-based catalysts, on the other hand, are more expensive, less selective, less durable, more prone to gas poisoning, and worse for the environment. As a productive, affordable, and metal-free substitute for platinum for oxygen reduction in fuel cells, a new class of catalyst based on earth-abundant carbon materials was discovered in 2009. Since then, significant advancements have been made, and an expanding number of catalytic processes have shown to benefit from carbon-based, metal-free catalysts. In the fields of polymer and material sciences, novel polymerizations based on alkyne monomers are developing into a potent tool to create polymers with distinctive structures and cutting-edge functions, and in recent decades, scientists have become interested in creating a variety of novel polymerizations. In this context, catalytic systems are crucial for influencing the effectiveness of polymerization and the properties of the resulting polymers.