approaches can combine both scenarios. In practice, both bottom-up and top-down scenarios are generally forced to fairly extreme model assumptions in order to account for current measurements. So, which ever approach turns out to be most relevant, we will learn some very interesting physics or astrophysics. The coming generations of cosmic ray detectors should tell us which direction to go within the next few years.

In addition to the other lectures from this School readers interested in more details or alternative perspectives may want to read some of the excellent reviews of this topic that have appeared recently in the literature (e.g., Olinto 2000; Watson, 2000; Sigl, 2002).

I begin my discussion with a short outline of some background that helps to define the underlying issues. My main goal is to confront the physics that must be included in cosmic Zevatrons, so §3 aims to find the underlying constraints that can be used to limit the field of models. Since many models accelerate particles in shock waves, I will follow with a short discussion of the physics of diffusive shock acceleration, before turning to apply the appropriate physical constraints to some candidate phenomena in §5.

Some Background
===============

The cosmic 