Homopolymers of olefin monomers having polar functional groups, and copolymers of these monomers with each other and with non-polar olefins and optionally carbon monoxide are disclosed. The polymers can be prepared by contacting the corresponsping monomers with a transition metal catalyst under comparatively mild conditions; this preserves at least some of the polar functional groups in the resulting polymer. The polymers are suitable for processing in conventional extrusion processes, and can be formed into high barrier sheets or films, or low molecular weight resins for use in synthetic waxes in wax coatings or as emulsions.