We show how sunspot activity and magnetic flux transport determine the evolution of coronal holes and their wind streams. Holes (open field regions) are located by applying a current-free coronal model to observations and simulations of the photospheric field. The sources of high-speed wind are inferred from an empirical relation between wind speed measured at 1 AU and the divergence rate of the coronal field. We find that supergranular diffusion is the primary transport process involved in the growth of open field regions and their wind streams. Meridional flow accelerates the decay of low-latitude holes by carrying flux to mid-latitudes, where rotational shear and diffusion combine to symmetrize the large-scale field; by concentrating the remaining flux at the poles, it also limits the size of the polar holes and the speed and latitudinal extent of their wind streams. The highest wind speeds (lowest flux-tube expansion rates) are associated with minimum-field regions such as those bordering neighboring holes of the same polarity. During the rising phase of the sunspot cycle, these areas lie between the mid-latitude active regions and the receding polar holes, so that relatively little high-speed wind reaches the ecliptic. Low wind speeds tend to occur at all latitudes with the disappearance of the polar holes at sunspot maximum. Just after sunspot maximum, fast polar "jets" are generated as trailing-polarity surges containing east-west oriented holes converge onto the poles and the last remnants of the old-cycle polar fields are cancelled. As sunspot activity declines and progresses to lower latitudes, trailing-polarity regions dominate in each hemisphere, and the distribution of open flux and high-speed wind reaches its greatest extent. Even near sunspot minimum, the fastest wind originates not from the centers of the polar holes but from their relatively weak-field extensions.