I will consider the quantum transport in networks of weakly disordered metallic wires. Quantum interferences of reversed trajectories are responsible for a small contribution to the conductance, known as the "weak localization correction" (WL). From the experimental point of view the study of the WL provides an efficient tool to probe phase coherence in weakly disordered metals. The WL is identified through its magnetic field dependence: for example, the conductance of a ring presents oscillations as a function of the flux with period $h/2e$, known as Al'tshuler-Aronov-Spivak (AAS) oscillations. The contributions of interfering reversed trajectories are encoded in the so-called "Cooperon". I will show how the Cooperon must be properly integrated into a multiterminal network connected to reservoirs and will emphasize the role on nonlocality of quantum transport.
In a second part I will discuss the effect of decoherence due to electron-electron interaction and more specifically how the AAS oscillations are affected by electron-electron interaction in several networks.