The combination of supramolecular functional systems with biomolecular chemistry has been a fruitful exercise for decades, leading to a greater understanding of biomolecules and to a great variety of applications, for example, in drug delivery and sensing. Within these developments, the phospholipid bilayer membrane, surrounding live cells, with all its functions has also intrigued supramolecular chemists. Herein, recent efforts from the supramolecular chemistry community to mimic natural functions of lipid membranes, such as sensing, molecular recognition, membrane fusion, signal transduction, and gated transport, are reviewed.