We use two-dimensional hydrodynamic simulations to study the formation of nuclear rings and nuclear spirals and the associated mass inflow rates at the centers of barred galaxies. We find nuclear rings form by the centrifugal barrier that the inflowing gas cannot overcome. The size of nuclear rings depend on various galaxy properties such as the bar strength, the bar pattern speed, and the bulge central density: they are smaller in galaxies with a stronger or slower bar, and with a more centrally concentrated bulge. Even a very weak bar potential can induce nuclear spirals that eventually develop into shocks. In galaxies with high shear, nuclear spirals are tightly wound and the shocks are inclined, forming a circumnuclear disk. On the other hand, galaxies with low shear produce loosely wound spirals and perpendicular shocks, without forming a circumnuclear disk. The mass inflow rates driven by the nuclear spiral shocks are enough to account for the observed level of AGN activities in Seyfert galaxies.