Understanding of cell membrane organization has evolved significantly from the classic fluid mosaic model. It is now recognized that biological membranes are highly organized structures, with differences in lipid compositions between inner and outer leaflets and in lateral structures within the bilayer plane, known as lipid rafts. These organizing principles are important for protein localization and function as well as cellular signaling. However, the mechanisms and biophysical basis of lipid raft formation, structure, dynamics and function are not clearly understood. One key question, which we focus on in this review, is how lateral organization and leaflet compositional asymmetry are coupled. Detailed information elucidating this question has been sparse because of the small size and transient nature of rafts and the experimental challenges in constructing asymmetric bilayers. Resolving this mystery will require advances in both experimentation and modeling. We discuss here the preparation of model systems along with experimental and computational approaches that have been applied in efforts to address this key question in membrane biology. We seek to place recent and future advances in experimental and computational techniques in context, providing insight into in-plane and transverse organization of biological membranes.