Many-electron effects in low-dimensional semiconductor structures: quantum wells, wires, and dots are discussed. Three examples are given: (a) the quasi-particles of a Fermi liquid are illustrated with the calculation of the self-energy of a hot electron coupled to plasmons and optical phonons in modulation doped quantum wells, (b) the Fermi edge singularity and (c) the incompressibłe states of strongly correlated electrons in quantum dots tunable by applied magnetic field.