High–energy accelerators and colliders have been essential tools in the search for the fundamental constituents of matter and their interactions. They have contributed greatly to the validation of the Standard Model. In the coming years, new data will be collected at HERA, the Tevatron and, starting in 2005, at LHC. Considering the fruitful complementarity of hadron colliders and lepton colliders, it is therefore desirable to extend the centre–of–mass energy of e+e− colliders from that presently obtained at LEP (ca. 200 GeV) into the TeV energy range, with luminosities well above 1034 cm−2 sminus;1. Such high energies and luminosities can only be reached using electron–positron linear colliders. The physics potential of a high–energy e+e− collider and the success of the Stanford Linear Collider have led to a worldwide coordinated effort to construct such a facility. Detailed design work as well as the construction of large test facilities is underway at many major particle physics laboratories. In this review, the physics potential and design of TESLA, a collider based on low–frequency superconduction radio frequency cavities, will be discussed.