The potential physiological relevance of liquid-liquid phase separation in lipid membranes to the formation and stability of “lipid rafts” in cellular plasma membranes has prompted extensive investigation of the physical chemistry underlying these phenomena. Furthermore, the concept of lipid rafts – 10-200 nm regions of cellular membrane enriched in specific lipids and proteins to enable complex processes – has led naturally to questions concerning the sorting of both lipids and proteins between membranes of different organelles within the cell, each with distinct lipid and protein composition. The shapes and, more specifically, the curvatures of membrane transport intermediates have been invoked to play a role in both lipid and protein sorting. In addition, lipid and protein composition may directly affect the membrane curvature. In this contribution, the line tension and dipole density differences between demixed fluid phases of monolayers comprised of dimyristoylphosphatidylcholine and dihydrocholesterol were investigated by measuring the two-dimensional thermal fluctuations of domain boundaries. These parameters are essential determinants of domain stability, and their quantification will yield an increased understanding of the physical processes responsible for aspects of lateral phase separation. Furthermore, phase-separated giant unilamellar vesicles from which are pulled thin cylindrical tubes are employed to understand domain nucleation in curvature gradients, complemented by measurements of the biophysical force required to pull such tubes. These results indicate that strong lipid-lipid interactions can lead to lipid sorting by curvature, as well as present diffusion barriers to enable selective sorting of lipids and proteins. Finally, the curvature generation of Drosophila amphiphysin N-BAR domain is quantitatively assessed through the tube-pulling assay as before but performed using homogenous lipid membranes. Fluorescently-labeled protein preferentially sorted into the high (positive) curvature of the tubes from the essentially flat vesicle. Furthermore, the measured tube force decreased to lower equilibrium values in a protein concentration-dependent manner. Future measurements on other BAR domains will improve upon previous qualitative comparisons of curvature generation ability. Collectively, the results provide quantitative assessment of several biophysical parameters underlying the lateral sorting of lipids and proteins.