Based on realistic mechanisms of Ca2+ buffering that include both stationary and mobile buffers, we derive and investigate models of Ca2+ diffusion in the presence of rapid buffers. We obtain a single transport equation for Ca2+ that contains the effects caused by both stationary and mobile buffers. For stationary buffers alone, we obtain an expression for the effective diffusion constant of Ca2+ that depends on local Ca2+ concentrations. Mobile buffers, such as fura-2, BAPTA, or small endogenous proteins, give rise to a transport equation that is no longer strictly diffusive. Calculations are presented to show that these effects can modify greatly the manner and rate at which Ca2+ diffuses in cells, and we compare these results with recent measurements by Allbritton et al. (1992). As a prelude to work on Ca2+ waves, we use a simplified version of our model of the activation and inhibition of the IP3 receptor Ca2+ channel in the ER membrane to illustrate the way in which Ca2+ buffering can affect both the amplitude and existence of Ca2+ oscillations.