Recent progress regarding the copolymerization of norbornene with various polar α-olefins catalyzed by nickel and palladium catalysts is reviewed here with special attention paid to the diverse catalyst frameworks, polar monomer scopes as well as polymer microstructures. Both the influences of steric effect and electron property of ligand substituents and the type of polar monomers on the catalytic behaviors (activity, stability, polarity tolerance, etc.) and the polymer microstructures (molecular weight and distribution, comonomer contents, etc.) have been summarized. The introduction of noncyclic-olefins, such as polar vinyl monomers, polar higher α-olefins, and polar styrenes, into rigid cyclic-based polynorbornene chain resulted in significant modifications on the polarity, compatibility, thermostability, processibility, transparency, and many other properties of the material, which has also been discussed in the review. The contents of this review have been classified according to the type of polar monomers involved in the norbornene copolymerization, and each section included nickel and palladium catalysts bearing different ligand structures, which will be meaningful for the development of new types of catalysts and new families of norbornene-based cyclic olefin copolymer materials in the future.