Polyolefin materials have huge annual output and wide applications, which are closely related to human production and life closely. The core of polyolefin research lies in the catalyst, the performance of which often determines the properties of polyolefins. Therefore, the design and synthesis of high-performance catalyst have become a hot research topic, and a large number of catalysts have come out. Cobalt complexes are very important kind of olefin polymerization catalysts, which can be used to catalyze a variety of monomer polymerization. These cobalt complexes are structure diversity and have a variety of coordination atoms (such as, N, O, P, S etc.), and the synthesis is relatively simple. Therefore, the structure of the catalyst can be precisely regulated to improve the catalytic activity, adjust the microstructure of the polymer, and improve the macroscopical properties of the polymer. In this paper, the applications of cobalt complexes in homopolymerization of ethylene, conjugated dienes, norbornene, acrylates and other common monomers are reviewed, and the cobalt complexes are classified from the perspective of structure. What's more, the effects of catalyst structure, temperature, cocatalyst on catalyst activity, polymer molecular weight and polymer microstructure are discussed in detail. It is expected to provide a reference for the design and synthesis of cobalt complexes in the future.