Butadiene rubber (BR) is one of the most useful and second most produced rubber worldwide. Polymerization of 1,3-butadiene (BD) is a highly stereospecific reaction that offers a wide variety of BR with different microstructures and influences the fundamental properties of the rubber. Since the first successful polymerization of conjugated diene using the Ziegler–Natta–based catalyst (TiCl4 or TiCl3 with aluminum alkyls) in 1954, the research on producing synthetic rubber with an appropriate catalyst system has been accelerated. Subsequently, various research groups are actively engaged in designing active catalyst systems based on a suitable combination of transition metal complexes with alkyl-aluminum and successfully using them in BD polymerization. Although various scientific inventions have proven their significance for the production of high-quality BR, with the rising demands in improving the quality of the product, research on developing new catalyst systems with enhanced catalytic activity and high stereoselectivity is still in progress. The present review focuses on the synthesis of BR using various transition metal catalysts and discusses their microstructures. The catalysts based on new-generation metal complexes with phosphorus, nitrogen, and oxygen donor ligands (e.g., phosphines, imines, 1,10-phenanthroline, and imino-pyridines) have been introduced. The role that catalysts play in the production of BR with different microstructures (i.e., high-cis, high-trans or low-cis, low-trans polybutadiene) has also been described. The combination of catalyst (transition metal complex) and suitable co-catalyst (alkyl-aluminum) is the major factor influencing the reaction and microstructure of the resulting polymer. This report focuses on the effect of transition metal catalysts (i.e., lithium [Li], titanium [Ti], zirconium [Zr], iron [Fe], cobalt [Co], nickel [Ni], and neodymium [Nd]) on the activity and stereoselectivity of polymers such as 1,4-cis-, 1,4-trans-, and 1,2-vinyl-polybutadiene.