The lattice cluster theory (LCT) is used to study the influence of structural and energetic asymmetries on the miscibilities of binary polyolefin blends. The theory describes monomer molecular structures by using a united atom model for the polyolefins, where each CHn united atom group occupies a single lattice site and where, for simplicity, both species in each blend are taken to have the same number (M) of carbons. In order to isolate the contributions from structural asymmetries, the phase diagrams are first computed for a simplified model in which all CHn united atom groups interact with the same microscopic energy (epsilon), a model for which Flory-Huggins theory would predict complete miscibility. The ratio of the calculated critical temperature (T-c) to the number (M) of carbon atoms per chain correlates very well with a blend topological index (r) defined in terms of the fractions of tri- and tetrafunctional carbon atoms in the chains. The presence of tetrafunctional carbons is directly responsible for the failure of an older rule of thumb for predicting blend miscibilities on the basis of the disparity in ratios of the numbers of end to interior !or total) carbon atoms per chain of the two blend components. Introducing energetic asymmetries into the LCT united atom model leads to a rich variety of phase behavior (with upper or lower critical temperatures, or even with both lying in an experimentally accessible range). The LCT computations display the same strong sensitivity of phase diagrams to small changes in the microscopic interaction energies as would arise from the Flory-Huggins theory. Computations of coexistence curves are used in conjunction with a recent compressible theory of interfacial properties to examine the influence of monomer structural asymmetries on the interfacial profiles, widths, and tensions in phase-separated polyolefin blends.