Dislocations exhibit a number of exceptional electronic properties resulting in a significant increase of the drain current of metal-oxide-semiconductor field-effect transistors (MOSFETs) if defined numbers of these defects are placed in the channel. Measurements on individual dislocations in Si refer to a supermetallic conductivity. A model of the electronic structure of dislocations is proposed based on experimental measurements and tight binding simulations. It is shown that the high strain level on the dislocation core-exceeding 10% or more-causes locally dramatic changes of the band structure and results in the formation of a quantum well along the dislocation line. This explains experimental findings (two-dimensional electron gas and single-electron transitions). The energy quantization within the quantum well is most important for supermetallic conductivity.