The general features of the cosmic-ray spectrum have been known for a long time. Although the basic approaches to understanding cosmic-ray propagation and acceleration have also been well understood for many years, there are several questions of great interest that motivate the current intense experimental activity in the field. If the energy-dependence of the secondary to primary ratio of galactic cosmic rays is as steep as observed, why is the flux of PeV particles so nearly isotropic? Can all antiprotons and positrons be explained as secondaries or is there some contribution from exotic sources? What is the maximum energy of cosmic accelerators? Is the "knee" of the cosmic-ray spectrum an effect of propagation or does it perhaps reflect the upper limit of galactic acceleration processes? Are gamma-ray burst sources (GRBs) and/or active galactic nuclei (AGN) accelerators of ultra-high-energy cosmic rays (UHECR) as well as sources of high-energy photons? Are GRBs and/or AGNs also sources of high-energy neutrinos? If there are indeed particles with energies greater than the cutoff expected from propagation through the microwave background radiation, what are their sources? The purpose of this lecture is to introduce the main topics of the School and to relate the theoretical questions to the experiments that can answer them.