  We survey some recent results about the order structure of various kinds of
ultrafilters. More precisely, we study Rudin-Keisler and Tukey reducibility in
classes of selective, stable ordered-union, and P-point ultrafilters. Although
these reductions are fundamentally different, there are connections between
them. On the other hand, even though the classes of ultrafilters we consider
are similar, there are significant differences in their order structure, as
will be seen in the survey.
