  A quantum dot is a sub-micron-scale conducting device containing up to
several thousand electrons. Transport through a quantum dot at low temperatures
is a quantum-coherent process. This review focuses on dots in which the
electron's dynamics are chaotic or diffusive, giving rise to statistical
properties that reflect the interplay between one-body chaos, quantum
interference, and electron-electron interactions. The conductance through such
dots displays mesoscopic fluctuations as a function of gate voltage, magnetic
field, and shape deformation. The techniques used to describe these
fluctuations include semiclassical methods, random-matrix theory, and the
supersymmetric nonlinear $\sigma$ model. In open dots, the approximation of
noninteracting quasiparticles is justified, and electron-electron interactions
contribute indirectly through their effect on the dephasing time at finite
temperature. In almost-closed dots, where conductance occurs by tunneling, the
charge on the dot is quantized, and electron-electron interactions play an
important role. Transport is dominated by Coulomb blockade, leading to peaks in
the conductance that at low temperatures provide information on the dot's
ground-state properties. Several statistical signatures of electron-electron
interactions have been identified, most notably in the dot's addition spectrum.
The dot's spin, determined partly by exchange interactions, can also influence
the fluctuation properties of the conductance. Other mesoscopic phenomena in
quantum dots that are affected by the charging energy include the fluctuations
of the cotunneling conductance and mesoscopic Coulomb blockade.
