Charge injection barriers at metal/polymer interfaces are affected by many factors, including the physical, chemical, and electronic structure of the metal, the polymer, and the interfacial region. Here, we consider a diverse set of metals (Al, Ag, Au, Pd, and Pt), and a few metal/polyethylene interfacial configurations in an attempt to span situations encountered in real metal/polyethylene systems. Several relevant electronic properties and the charge injection barriers are computed for these cases using density functional theory computations. The calculations reveal important trends and correlations, and identify the favored mechanism of charge transport (as mediated by the charge injection barriers). While satisfactory correspondences of the computations with available measurements are achieved, quantitative discrepancies still remain between the computed and measured injection barriers. These issues may be resolved when more realistic models of the interface, inclusive of its morphological complexities, are utilized.