Spiders can produce cobwebs with high strength to density ratio and surprisingly display self-cleaning, strong and releasable adhesion (like geckos). Nanointerlocking, capillary and van der Waals forces, all potential adhesive mechanisms, are thus discussed, demonstrating the key role played by hierarchy in the design of superhydrophobic, i.e. self-cleaning (dry or wet and enhanced by activating Fakir drops as in lotus leaves) and superadhesive materials. The reversibility of the strong attachment is quantified thanks to an improved nonlinear peeling model including friction, for which the solution in closed form is provided. Thus, mimicking nature, thanks to carbon-nanotube-based technology, we suggest the feasibility of large invisible cables, as well as of self-cleaning, superadhesive and releasable hierarchical smart materials. We found that a man can theoretically be supported by a transparent cable with cross-section of 1 cm² and feasibly, with spider material gloves and boots, could remain attached even to a ceiling: a preliminary step towards a Spiderman suit.