Diffraction of Protons and Nuclei at High Energies

We review the description of high energy diffraction from both the s and t channel viewpoints, and demonstrate their consistency. We emphasize the role played by s channel unitarity and multi-Pomeron exchanges. We explain how these effects suppress hard diffractive processes. As examples, we describe the calculation of diffractive dijet production at the Tevatron and predict some of the rich diffractive phenomena accessible in proton-nuclear collisions at RHIC