  A brief overview is presented of recent work which investigates the
time-dependent relaxation of charge and its spontaneous fluctuations on
mesoscopic conductors in the proximity of gates. The leading terms of the low
frequency conductance are determined by a capacitive or inductive emittance and
a dissipative charge relaxation resistance. The charge relaxation resistance is
determined by the ratio of the mean square dwell time of the carriers in the
conductor and the square of the mean dwell time. The contribution of each
scattering channel is proportional to half a resistance quantum. We discuss the
charge relaxation resistance for mesoscopic capacitors, quantum point contacts,
chaotic cavities, ballistic wires and for transport along edge channels in the
quantized Hall regime. At equilibrium the charge relaxation resistance also
determines via the fluctuation-dissipation theorem the spontaneous fluctuations
of charge on the conductor. Of particular interest are the charge fluctuations
in the presence of transport in a regime where the conductor exhibits shot
noise. At low frequencies and voltages charge relaxation is determined by a
nonequilibrium charge relaxation resistance.
