The copolymerization of ethylene with polar monomers has been heavily studied.  The high oxophilicity of the early metals precluded their use in this application.
Efforts to copolymerize polar comonomers led to catalysts based upon nickel and palladium, inspired by the success of the Shell Higher Olefin Process.  Typical post-metallocene catalysts feature bulky, neutral, alpha-diimine ligands.   DuPont commercialized the Versipol olefin polymerization system.  Eastman commercialized the related Gavilan technology.  These complexes catalyze the homopolymerize ethylene to a variety of structures that range from high density polyethylene through hydrocarbon plastomers and elastomers by a mechanism referred to as “chain-walking”. By modifying the bulk of the alpha-diimine, the product distribution of these systems can be tuned to consist of hydrocarbon oils (alpha-olefins), similar to those produced by more tradition nickel(II) oligo/polymerization catalysts.  As opposed to metallocenes, they can also randomly copolymerize ethylene with polar comonomers such as methyl acrylate.
A second class of catalysts feature mono-anionic bidentate ligands related to salen ligands. and DuPont. 
The concept of bulky bis-imine ligands was extended to iron complexes  Representative catalysts feature diiminopyridine ligands.  These catalysts are highly active but do not promote chain walking. The give very linear high-density polyethylene when bulky and when the steric bulk is removed, they are very active  for ethylene oligomerization to linear alpha-olefins.
A salicylimine catalyst system based on zirconium exhibits high activity for ethylene polymerization.  The catalysts can also produce some novel polypropylene structures.  Despite intensive efforts, few catalysts have been successfully commercialized for the copolymerization of polar monomers.