Cationic lipid-DNA complexes, often referred to as lipoplexes, are formed spontaneously in aqueous solutions upon mixing DNA and liposomes composed of cationic and nonionic lipids. Understanding the mechanisms underlying lipoplex formation, structure and phase behavior is crucial for their further development and design as non-viral transfection vectors in gene therapy. From a physical point of view, lipoplexes are ordered, self-assembled, composite aggregates. Their preferred spatial geometry and phase behavior are governed by a delicate coupling between the electrostatic interactions which drive lipoplex formation and the elastic properties of the constituent lipid layers, both depending on the molecular nature and composition of the lipid mixture. In this review we outline some recent efforts to model the microscopic structure, energetic and phase behavior of cationic lipid-DNA mixtures, focusing on the two principal aggregation geometries: the lamellar (Lα C), or “sandwich” complexes, and the hexagonal (HII C), or “honeycomb” complexes. We relate the structural and thermodynamic properties of these two “canonical” lipoplex morphologies to their appearance in phase diagrams of DNA-lipid mixtures, emphasizing the crucial role fulfilled by the molecular packing characteristics of the cationic and neutral lipids, as reflected in the curvature elastic properties of the mixed lipid layer.