<p>Coordination-insertion copolymerization of ethylene with polar vinyl monomers offers a direct route to functionalized polyolefins, enabling regular incorporation of polar groups under mild conditions and superior microstructural control compared with post-functionalization or radical routes. The persistent polar monomer problem—the tendency of polar groups to coordinate to or poison active metal sites—motivates the focus on late-transition-metal catalysts, chiefly Ni and Pd. Recent advances in ligand design, catalyst engineering, and monomer modification have improved comonomer incorporation, suppressed chain transfer, and enhanced thermal robustness. Mechanistic studies now resolve 2,1- versus 1,2-insertion, ligand-induced chelate isomerization, and polar-monomer-promoted chain-transfer pathways. This feature article surveys nickel- and palladium-based catalytic systems reported from 2020 onward for copolymerization of ethylene with fundamental polar monomers, with an emphasis on acrylates, while also covering acrylic acid, vinyl acetate, butyl vinyl ether, acrylonitrile, acrylamide, vinyl silyl ethers, and selected disubstituted monomers, categorizing recent advances by key ligand classes ([N,N], [N,O], [P,O]) and linking mechanism, selectivity, and polymer properties to guide catalyst design and scale-up.</p>