It is shown that the dephasing rate in Coulomb coupled mesoscopic structures is determined by charge relaxation resistances. The charge relaxation resistance together with the capacitance determines the RC-time of the mesoscopic structure and at small frequencies determines the voltage fluctuation spectrum. Self-consistent expressions are presented which give the charge relaxation resistance and consequently the dephasing rate in terms of the diagonal and off-diagonal elements of a generalized Wigner-Smith delay-time matrix. Dephasing rates are discussed both for the equilibrium state and in the transport state in which charge fluctuations are generated by shot noise. A number of different geometries are discussed. This article is to appear in {\it Quantum Mesoscopic Phenomena and Mesoscopic Devices}, edited by I. O. Kulik and R. Ellialtioglu, (Kluwer, unpublished).