Abstract: A number of particularly interesting low-dimensional codes and lattices have the extra property of being equal to (or, for lattices, similar to) their duals; as a result, it is natural to wonder to what extent self-duality constrains the minimum distance of such a code or lattice. The first significant result in this direction was that of Mallows and Sloane, who showed that a doubly-even self-dual binary code of length n has minimum distance at most $4\lfloor n/24\rfloor+4$, and with Odlyzko, obtained an analogous result for lattices. Without the extra evenness assumption, they obtained a much weaker bound; in fact, as I will show, this gap between singly-even and doubly-even codes is illusory: the bound $4\lfloor n/24\rfloor+4$ holds for essentially all self-dual binary codes. For asymptotic bounds, the best result for doubly-even binary codes is that of Krasikov and Litsyn, who showed $d\le Dn+o(n)$ where $D = (1-5^{-1/4})/2 \sim 0.165629$. I'll discuss a different proof of their bound, applicable to other types of codes and lattices, in particular showing that for any positive constant $c$, there are only finitely many self-dual binary codes satisfying $d\ge Dn-c\sqrt{n}$.