Late-transition-metal catalysts have great potentials to incorporate polar comonomers during olefin polymerization. The preparation of polar-functionalized polyolefins with different microstructures and topologies is a highly fascinating concept. In this contribution, we demonstrate this possibility through palladium-catalyzed ethylene copolymerizations with polar-functionalized α-olefins and their terpolymerizations with α-olefins. A phosphine–sulfonate–palladium catalyst (PO-Pd) afforded highly linear polyethylene during ethylene homopolymerization. Linear low-density polyethylene (LLDPE) was obtained from the PO-Pd-catalyzed copolymerizations of ethylene with α-olefins; in these copolymerizations, the partial or complete replacement of α-olefins with polar-functionalized α-olefins led to the formation of polar-functionalized LLDPE (P-LLDPE). A specially designed α-diimine palladium catalyst (NN-Pd) afforded polyethylenes with tunable branching densities (16–37 per 1000 carbon atoms), melting points (101–113 °C), and densities (0.89–0.92 g/cm3), which closely resemble those of low-density polyethylene (LDPE). The NN-Pd-catalyzed copolymerizations of ethylene with polar α-olefins generated analogues of polar-functionalized low-density polyethylene (P-LDPE). The mechanical and surface properties of these polar polyolefin materials were studied in detail, and their properties were further improved/modified through cross-linking reactions.