Compartmentalization is crucial for the evolution of life. Present-day phospholipid membranes exhibit a high level of complexity and species-dependent homochirality, the so-called lipid divide. It is possible that less stable, yet more dynamic systems, promoting out-of-equilibrium environments, facilitated the evolution of life at its early stages. The composition of the preceding primitive membranes and the evolutionary route towards complexity and homochirality remain unexplained. Organics-rich carbonaceous chondrites are evidence of the ample diversity of interstellar chemistry, which may have enriched the prebiotic milieu on early Earth. This Review evaluates the detections of simple amphiphiles - likely ancestors of membrane phospholipids - in extraterrestrial samples and analogues, along with potential pathways to form primitive compartments on primeval Earth. The chiroptical properties of the chiral backbones of phospholipids provide a guide for future investigations into the origins of phospholipid membrane homochirality. We highlight a plausible common pathway towards homochirality of lipids, amino acids, and sugars starting from enantioenriched monomers. Finally, given their high recalcitrance and resistance to degradation, lipids are among the best candidate biomarkers in exobiology.