  We perform a brief but critical review of the Landauer picture of transport
that clarifies how decoherence appears in this approach. On this basis, we
present different models that allow the study of the coherent and decoherent
effects of the interaction with the environment in the electronic transport.
These models are particularly well suited for the analysis of transport in
molecular wires. The effects of decoherence are described through the
D'Amato-Pastawski model that is explained in detail. We also consider the
formation of polarons in some models for the electron-vibrational interaction.
Our quantum coherent framework allows us to study many-body interference
effects. Particular emphasis is given to the occurrence of anti-resonances as a
result of these interferences. By studying the phase fluctuations in these
soluble models we are able to identify inelastic and decoherence effects. A
brief description of a general formulation for the consideration of
time-dependent transport is also presented.
