  This is a review of the phase coherent transmission through interacting
mesoscopic conductors. As a paradigm we study the transmission amplitude and
the dephasing rate for electron transport through a quantum dot in the Coulomb
blockade regime. We summarize experimental and theoretical work devoted to the
phase of the transmission amplitude. It is shown that the evolution of the
transmission phase may be dominated by non-universal features in the short-time
dynamics of the quantum dot. The controlled dephasing in Coulomb coupled
conductors is investigated. Examples comprise a single or multiple quantum dots
in close vicinity to a quantum point contact. The current through the quantum
point contact "measures" the state of the dots and causes dephasing. The
dephasing rate is derived using widely different theoretical approaches. The
Coulomb coupling between mesoscopic conductors may prove useful for future work
on electron coherence and quantum computing.
