We first present a general overview of Venn diagrams and their
properties and uses, focusing on diagrams with rotational
symmetry, which can be quite beautiful.
We then discuss some recent results about Venn diagrams.
Killian, Griggs, and Savage proved that symmetric Venn
diagrams exist if and only if the number of curves, , is prime.
However, the resulting diagrams are highly non-simple, where a
simple diagram is one with at most two curves passing through any point.
In fact, the KGS diagrams are minimal with respect to number of
intersection
points within the class of diagrams drawable with convex curves, since
they have
points of intersection.
We show how to modify their construction so that the resulting
diagrams are ``half-simple" in the sense of having asymptotically
points of intersection, whereas a simple diagram has
points of intersection.
Time permitting, we also present
some recent constructions of pseudo-symmetric and area-proportional
Venn diagrams.