Biopolymers fulfil a variety of different functions in nature. They conduct various processes inside and outside cells and organisms, with a functionality ranging from storage of information to stabilization, protection, shaping, transport, cellular division, or movement of whole organisms. Within the plethora of biopolymers, the most sophisticated group is of proteinaceous origin: the cytoskeleton of a cell is made of protein filaments that aid in pivotal processes like intracellular transport, movement, and cell division; geckos use a distinct arrangement of keratin-like filaments on their toes which enable them to walk up smooth surfaces, such as walls, and even upside down across ceilings; and spiders spin silks that are extra-corporally used for protection of offspring and construction of complex prey traps. The following tutorial review describes the hierarchical organization of protein fibers, using spider dragline silk as an example. The properties of a dragline silk thread originate from the strictly controlled assembly of the underlying protein chains. The assembly procedure leads to protein fibers showing a complex hierarchical organization comprising three different structural phases. This structural organization is responsible for the outstanding mechanical properties of individual fibers, which out-compete even those of high-performance artificial fibers like Kevlar. Web-weaving spiders produce, in addition to dragline silk, other silks with distinct properties, based on slightly variant constituent proteins--a feature that allows construction of highly sophisticated spider webs with well designed architectures and with optimal mechanical properties for catching prey.