  This thesis describes the merging of the two fields of Coulomb drag and
mesoscopic physics. The thesis presents a theory for Coulomb drag between two
mesoscopic systems based on linear-response theory. The formalism expresses the
drag in terms of either scattering matrices and wave functions or Green
functions, and its range of validity covers both ballistic and disordered
phase-coherent systems. The consequences are worked out either by analytic
means, such as the random matrix theory, or by numerical simulations. The
formalism is applied to i) drag between mesoscopic quantum wires and ii) drag
between mesoscopic quantum dots. In these systems it is found that for even
weak disorder the mesoscopic sample-to-sample fluctuations of the drag
conductance can be of the order of - or even exceed - the mean value. Depending
on the particular disorder configuration this is giving rise to a possible sign
change of the induced current.
