Configurations of ovals

Abstract.

We survey the known hyperovals in $\mathrm{PG}(2,q)$. We then survey the relationship of the study of configurations of ovals in $\mathrm{PG}(2,q)$ called augmented fans to that of ovoids of $\mathrm{PG}(3,q)$, flocks of the quadratic cone of $\mathrm{PG}(3,q)$, flocks of a translation oval cone of $\mathrm{PG}(3,q)$ and spreads of certain generalised quadrangles of order$q$. We also consider the configurations of ovals in$\mathrm{PG}(2,q)$ called herds and their relationship with flocks of the quadratic cone of$\mathrm{PG}(3,q)$.