Liposomes, which consist of bilayer lipids surrounding interior aqueous compartment(s), were first characterized nearly 60 years ago. Remarkably, many fundamental properties of liposomes and their micellar-like "solid core" counterparts (a lipid monolayer surrounding a hydrophobic core) and transitions between these structures remain poorly understood. In this work, we examine the effects of basic variables on the morphology adopted by lipid-based systems produced by rapid mixing of lipids in ethanol with aqueous media. We show that, for lipids such as distearolyphosphatidylcholine (DSPC)-cholesterol mixtures that form bilayer vesicles on hydration, osmotic stress can induce regions of high positive membrane curvature, leading to fusion between unilamellar vesicles to produce bilamellar vesicles. Addition of lyso PC, an "inverted cone"-shaped lipid that supports regions of high positive curvature, can inhibit the formation of these bilamellar vesicles by stabilizing a hemifused intermediate structure. Conversely, the presence of "cone"-shaped lipids such as dioleoylphosphatidylethanolamine (DOPE) that results in negative membrane curvature promotes fusion events subsequent to vesicle formation (during the ethanol dialysis stage), leading to bilamellar and multilamellar systems even in the absence of osmotic stress. Alternatively, the presence of increasing amounts of triolein, a lipid that is insoluble in lipid bilayers, results in increasing internal solid core structures until micellar-like systems with a hydrophobic core of triolein are achieved. These results are interpreted in terms of the intrinsic membrane curvature that bilayer vesicles can stably maintain as well as the ability of bilayer lipids to first form a monolayer around a solid core of hydrophobic material such as triolein and then, as the proportion of bilayer lipids is increased, progressively form bilayer structures that can eventually form a complete bilayer encapsulating both a hydrophobic core and an aqueous compartment. These hybrid intermediate structures may have utility as novel drug delivery systems.