Phospholipid membranes are versatile structures for mimicking biological surfaces. Bilayer and monolayer membranes can be formed on solid supports, leading to enhanced stability and accessibility of the biomimetic molecular film. This has facilitated functional studies of membrane proteins and aided the development of membrane-based applications in, for example, biosensing, self-assembled reaction kinetics and catalysis. Assembly and preparation of lipid films on supporting surfaces is a challenging engineering task with the goal of fabricating mechanically, chemically and thermodynamically stable lipid membranes. In this review, the current state of the art of molecularly thin lipid layer fabrication is presented with an emphasis on support materials, film formation mechanisms, characterisation methods, and applications.