Saturated hydrocarbon polymers may be differentiated by the relative amount and placement of methylene, methyl, methine, and quaternary carbon moieties. While it has been known or suspected for some time that polyolefins of conventional molecular weight (M-omega approximate to 100 kg/mol) with dissimilar chemical microstructures are most often immiscible in the liquid state, recent experiments with binary blends of model polyolefins have increased greatly our understanding of thermodynamic interactions between unlike chains. Model systems with methyl (-CH3) and ethyl (-C2H5) short-chain branches give results, expressed as the Flory-Huggins interaction parameter chi, that are nearly universal; repulsive interactions (chi > 0) are more pronounced at low temperatures, leading to liquid-liquid phase separation at an upper critical solution temperature. Phase behavior of more complex systems (with distributions of chain microstructures and/or molecular weight ) is generally consistent with predictions from model systems. An interesting exception is from work at Bristol on blends of Lightly branched ethylene - alpha-olefin copolymers with unbranched polyethylene as the minority species. Here the presence of two liquid phases is inferred under conditions not expected from model studies; effects of copolymer composition and molecular weight are also unusual. Recent theoretical work points to the importance of chain stiffness (established by short-chain branching) in determining the thermodynamics of model blends. Nonrandom mixing of chains with different stiffness gives rise to an enthalpic chi, which may be negative under certain conditions. Other limitations of the Flory-Huggins approach to describing blend energetics are considered. At present there is no theoretical basis for liquid-liquid phase separation reported by the Bristol group.