Recent experimental studies on supported lipid bilayers and giant vesicles have shown that uni-lamellar membrane systems can undergo spontaneous tubulation, i.e., can form membrane tubules or nanotubes without the application of external forces. In the case of supported lipid bilayers, the tube formation was induced by the adsorption of antimicrobial peptides. In the case of giant vesicles, spontaneous tubulation was observed after the polymer solution inside the vesicles underwent phase separation into two aqueous phases. Here, these processes are studied theoretically and shown to be driven by membrane tension generated by spontaneous curvature. The latter curvature is estimated for different types of adsorbing particles, such as ions, small molecules, and macromolecules, that differ in their size and in their adsorption kinetics. When the two sides of the membranes are exposed to two different concentrations of these particles, the membranes will acquire a spontaneous (or preferred) curvature. Particularly large spontaneous curvatures are induced by the adsorption of amphipathic peptides and BAR domain proteins. Another mechanism that induces spontaneous curvature is provided by different depletion layers in front of the two sides of the membranes. Irrespective of its molecular origin, a spontaneous curvature is predicted to generate a tension in weakly curved membranes, a 'spontaneous' tension that can vary over several orders of magnitudes and can be as high as 1 mJ m(-2). The concept of spontaneous tension is first used to explain the spontaneous tubulation of supported lipid bilayers when exposed to adsorbing particles. This tubulation process is energetically preferred when the spontaneous tension exceeds the adhesive strength of the underlying solid support. Furthermore, in the case of giant vesicles, the spontaneous tension can balance the osmotic pressure difference between the interior and exterior aqueous compartment. The vesicles are then able to form stable cylindrical nanotubes that protrude into the vesicle interior as observed recently for membranes in contact with two aqueous polymer phases. In these latter systems, the vesicle membranes are governed by two spontaneous tensions that can be directly measured since they are intimately related to the effective and intrinsic contact angles.