  The project of Greenlees et al. on understanding rational G-spectra in terms
of algebraic categories has had many successes, classifying rational G-spectra
for finite groups, SO(2), O(2), SO(3), free and cofree G-spectra as well as
rational toral G-spectra for arbitrary compact Lie groups.
  This paper provides an introduction to the subject in two parts. The first
discusses rational G-Mackey functors, the action of the Burnside ring and
change of group functors. It gives a complete proof of the well-known
classification of rational Mackey functors for finite G. The second part
discusses the methods and tools from equivariant stable homotopy theory needed
to obtain algebraic models for rational G-spectra. It gives a summary of the
key steps in the classification of rational G-spectrain terms of a symmetric
monoidal algebraic category.
  Having these two parts in the same place allows one to clearly see the
analogy between the algebraic and topological classifications.
